First, the fast ten cent quickie tour. Then a real-world photo example showing the principle. Then all the text you could want...
Novices always assume their camera meters ought to always give the correct exposure, but alas, they need to learn that life is not that simple. Meters are pretty dumb, and metering is an art done by the photographer.
Camera light meters (reflected meters) expose to make all pictures average out to be a middle tone. The beach scene, the macro of the spider, the studio portrait, or whatever... the reflective meter's goal is that overall, the metered area averages out to a middle tone (I call it middle gray, but it could be colored). And fortunately, a middle tone is often near about correct (most scenes are near average range), but the meter cannot distinguish those that do from those that don't. In those that don't, the meter can only see the light reflected from the scene, which is a lot of light if from white or light colors (so exposure is turned down), or not much light if reflected from black or dark colors (so exposure is turned up). The camera cannot tell the difference, it just sees some light, so it makes all pictures average out a middle gray (the only possible goal - not too dark, and not too bright). So photograph something all black, or something all white, and both come out near middle tone too, neither of which is correct in those cases. You need to be aware of this, it is simply how life is, how things work. Shown next below.
A Gray card, a Black card, and a White card photographed
These three cards (two are fun foamies) really are black and white and gray, here propped up on a couch background. This combined overall scene more nearly averages out to actually be middle gray (averaging a middle tone) - more what light meters expect to see, so its exposure is relatively correct. Reflective light meters simply try to make every scene average out to middle tone. The overall average tone is not too dark, not too light.
Black card with TTL flash (result is not black).
The metering used much more flash power (exposure) to make the black card be middle gray (tone). It makes couch and pink paper be white.
White card with TTL flash (result is not white).
The metering used much less flash power (exposure) to make the white card be middle gray (tone). Makes couch black, and pink paper dark.
Gray card with TTL flash
Approximately correct. The small paper was in fact pink, and the couch looks normal. Middle gray is made to be middle gray (tone), which is merely coincidence here. All images are always made to be middle tone average - that is all a reflective meter can do.
Get some black and white paper (from craft store, or any dark and light objects), and try this yourself, to see it, to believe it, and to understand and expect it.
This is simply what reflected light meters do. It is very good to know and expect this.
That was flash above. Now here are the same cards, repeated in a lawn chair outdoors in bright sun (no flash), same thing. It works the same way. This subject is not just about flash, it is about reflective light meters (like in cameras). This set is all automatically metered (without adjustment) by D300 camera in A mode (aperture preferred), f/8 ISO 320.
Three cards, f/8, 1/1250 second
Nearly exactly Sunny 16
Black card, f/8 1/200 second (result is not black)
Result is 2.3 stops overexposed, from first one.
White card, f/8 1/5000 second (result is not white)
Result is two stops underexposed, from first one.
18% gray card, f/8 1/800 second
Result is 1/3 stop over first one.
Any and all scenes will be metered to come out middle tone (average value of the metered area, not too dark, not too light). This is simply what reflected light meters do. It is very good to know and expect this. The exaggerated plain card background scene is used here to simply make it trivially easy to see this. These cards are not typical scenes. Any real scene will have mixed brightness areas (mountain and sky and green trees, etc), so that even unusually light or dark real subjects will rarely need as much as the two stops compensation these two "unreal" all white and all black subjects need (to actually be white or black). But it is routinely true that using reflective meters, light colored subjects (higher reflectivity) likely will need 1/2 stop or 1 stop more exposure to make them be light. Dark colored subjects (less reflective) likely will need 1/2 stop or 1 stop less exposure to make them be dark. The closer to middle gray the subject averages, the more accurate the reflected meter reading.
Typical or average wide range scenes do often average out about this same middle tone the meter expects, so it often works. It is the basis of the system, on average, it can often work. Just not always, and in varying degree even then.
NOTE: When I often mention result is middle gray here, I merely mean middle tone... it might have a red or green or blue tint sometimes, but the average of a wide range scene actually is often near neutral color. Middle tone has been called middle gray for decades, B&W film habit I guess, please forgive my quirk. In these cases, I don't necessarily mean the color "gray". And I don't mean center of the histogram either, peak will likely be a bit lower. I just mean the meter's goal is to create a middle tone (average of its metered area), not too dark, and not too light. Which is often reasonable, about right. But the problem comes when the subject ought to instead be dark or light - it won't be. It will always be more middle.
Here is a quick rose, intended to mimic some real photo scene. It is always photographed here with the same settings (here, automatic point&shoot TTL flash). The ONLY difference in these next pictures below is that the background is modified, regarding the white and black paper background (both are shown here first - ordinary white and black craft paper). All else is the same. The camera is aimed at the subject, and TTL automation takes over to expose the picture. The camera's TTL reflective meter sees different scenes differently. This is something worth knowing.
Nikon D300, ISO 200, f/8, 1/200 second, Matrix metering at about three feet. No adjustments were made, except as noted. These are all full DX frame (no cropping).
SB-800, direct flash, off camera, on a hot shoe cord, but at same distance as the lens. Automatic TTL metering mode. My own notion is that I like Center Weighted metering better, and the important subject is in the center, but this is Matrix metering, and there won't be much difference. The same concepts still apply.
This first one meters halfway reasonably, because the white and black do average out closer to middle gray, and the reflective meter is going to expose to make all scenes come out averaging middle gray. Most average or typical scenes do contain a wide range of tones, and do in fact average out near middle gray. Which is good, because that is how reflective meters work. However, not all scenes are "typical", so we simply pay attention, and do what we see we need to do.
To make it be real clear and obvious, let's just adjust the background a little at time, all else stays the same (but still with automatic TTL metering of the flash). At each frame, the ONLY difference was that the black paper was shifted left a little, and then the shutter button was pressed again. Then the TTL metering reacted to the new scene. This is how reflective metering works. This is the expected result. You can count on it.
The meter is "correct" on all of them, but the meter may be doing something different than you expect. It only does what it can do. The meter has absolutely no clue what any of this is, what it means, or how it ought to be. The meter cannot recognize a rose from a polar bear. Our human brain has smarts and experience to know immediately, what it is, and how it ought to be, so that is our natural expectation. But the meter only sees a blob of light, which it can measure, but without any understanding about what it is, or what it means, or how it should be. What it will be is a middle tone average. Those who imagine their camera meter should always give the correct exposure are simply in for big disappointments. Instead, the trick is in learning what it actually does, so we can use it as a good guide.
Speaking of reflective meters (camera meters), its method is, if more dark area, make it brighter. If more light area, make it darker. This is simply because - its only capability is to make the metered area of all pictures average out to be a middle tone, which is "correct" by its rules, but it may or may not be the result you want. Repeat after me: "There is absolutely no possible way a dumb computer can recognize the scene, and have any clue about the result that your human brain knows to expect." The reflected meter can only assume we want everything middle tone, whatever it is, just not too dark, and not too bright. The rest is up to us, and Exposure Compensation and/or Flash Compensation is how we control the dumb automation.
I normally always use Center Weighted metering, because I can nearly understand what it is going to do. However, this was Matrix metering, because it is popular, even if we cannot understand what it does. But Matrix does not change the main goal of how reflective light meters work. It meters the ambient, and then TTL meters the flash. Nikon flash meters its own area in the center of the frame. My notion is that it is a middle size spot there. Ambient may be a little different case, but speaking of TTL flash indoors (insignificant ambient), any mode Spot, Matrix, or Center will give the same result. TTL or TTL BL either, but remember that TTL BL changes to be TTL in Spot mode - you may see the TTL change. Check this out for yourself, it only takes a few seconds. Camera on a tripod so nothing changes. TTL flash, set the metering mode, click, change mode, click, change mode, click.
The effect of a large area of light color is that the light colors become middle tones (darker, underexposure). The effect of a large area of dark color is that the dark colors become middle tones (lighter, overexposure). The only possible goal is middle tones. You can repeat this same type of test too, and you should repeat it, so you can see and believe it, and understand it, and be able to use it. This is indeed a LOT to know.
I am trying real hard to get your attention. If you want to resist, then imagine me shaking you by your shoulders shouting "wake up". :) We really ought to know how the light meter works. This is all also true in sunlight too, but flash differences seem more pronounced (due to inverse square law falloff). The trick to know is that Flash Compensation is how we control TTL flash. Simply watch, and do what you see you need to do. Flash Compensation will greatly improve your TTL flash pictures.
Again, if any doubts, then it is absolutely necessary that you repeat this, do and see this kind of test in your own situation. It is real. It is how things work. All you need to repeat this is a sheet of black paper and a sheet of white paper, and your camera as a light meter. Then you can see, and believe, and will understand how it must influence your procedures.
We hear novices complain about such things, thinking that their meter is misbehaving, when they simply don't understand how reflective light meters work. They may have a little more to learn, but it is easy if we simply pay attention. The meter's goal in life is NOT to give "correct" exposure. The dumb meter has absolutely no clue how to do that. It has no clue even what the scene is, or how it ought to be, so there is never any concept of a "correct" reflective meter reading. The meter's goal in life is simply to expose all scenes to create a middle tone average, however much that takes, for whatever it is, regardless if we will agree that middle tone is precisely "correct" or not. The five rose scenes above have five different contents, with five different average values. The reflective meter's goal in life is to make all pictures average out to be a middle tone (speaking of the central metered area). Therefore, the TTL automation exposes each picture of a different scene differently, to make that middle tone result be true (average of the metered area). So dark scenes are exposed more, and light scenes are exposed less, to achieve the same middle tone every time.
This is simply how reflective meters work (and it is a good thing to understand and expect this). Note that the photographer's job is to sense if this current scene is darker or lighter colors than normal, i.e., if this exposure is going to need our help to come out darker or lighter as it should. This is easy today, the digital camera shows the result to us, then and there, while we can still correct it. When you know why, you also know how, so this is easy, no big deal at all. You will soon already "just know" before you take the picture, what to expect, and what to do about it... it quickly becomes second nature.
Details get in the way of the big picture. This subject is not about the background as such. It is more likely about the subject's own colors, but could be anything in the scene that the meter is metering. And it is not about "gray" as such. I say middle gray, from the B&W film days, but I simply mean any middle tone, usually near gray, but which sometimes might be red or green or blue, depending on how the actual colors in the metering area average together. My middle gray term also does not mean center of histogram, and it does not mean 18% (which are not the same thing anyway). It just means a middle tone. Not too dark, and not too light. A middle tone is likely more usable.
We could of course use Spot Metering, to isolate metering this rose from its background tones. However, we should understand that all this does is to make the smaller metered spot come out as a middle tone too (this is what meters do). There can be advantage of that, but it is also not necessarily "correct" - it just means that "middle tone" of this spot can be promised then (because that's how meters work). But of course a brighter subject should be brighter, and a darker subject should be darker, so either we must select the correct spot to become middle tone, or we must apply the expected compensation anyway. It is the photographers job to keep this straight, the reflected meter cannot do it.
The meaning of the meter's "averaging the picture to come out near middle gray" is something like this (these are the same five rose pictures):
The Photoshop Blur - Average filter numerically averages all pixels in the selected area to all be one average value, and its results on these last five are shown. The camera light meter exposes each so that each comes out middle gray level, in a similar way.
My try here is very crude, there are differences in the real world. I drew some circles to represent metering a center area - because that seemed possible to do - but the photos have already been taken, and are already light or dark because of that. The original images had been cropped slightly smaller in post processing too. So there are differences in size and location of the metered area which was actually metered. So this result shown only tries to imply the meter sees an area, and exposes so the average in that scene's area comes out about the middle gray, regardless. Hoping you will see the idea, rather than the details. The five circles did not all come out exactly the same gray shade here, but they would if we could actually match the same metered area. But it is not too far off, if you try just a little.
The point is that reflective meters expose to cause all images to come out near an averaged middle tone in a similar way, which is what I mean when I say a middle gray result. I don't necessarily mean the color gray, and if it is a picture of all green foliage, or all blue sky, it will be a bit green or blue, but many wide range pictures are often close to gray (and B&W film was gray). This one is a bit pink, which the color is not important, but the averaged middle tone is, as if it were gray.
When the camera exposure makes the metered area come out a middle shade, the rest of the picture necessary has to become lighter or darker, depending on what was in that metered area.
If the content of that metered area is dark colored like black (not very reflective), then it appears darker, so the frame will be overexposed to raise its metered area average to the middle tone.
If the content of that metered area is light colored like white (more reflective), then it is brighter, and will be underexeposed to lower its metered area to average to the middle tone.
All of these imagined metered areas ought to come out the same middle gray, which is what light meters do. So this averaged area may or may not give the actual "correct" exposure, which still depends entirely on the subject content in front of the camera (and the area of it that the meter is considering). Meters simply don't know what the scene is, or how it ought to be. They just see a spot of light, which will be made to come out middle tone. All they can do is to always try to create a middle tone result, regardless. The current scene might fit that model well if it is of average wide content, or maybe not. Which is OK, the human photographer is there to help, with his eyes and brain and experience. Digital makes it easy today.
There is more detail below, but the point is, assuming the common reflective meter, what reading that you meter depends on what you are metering. You, as the photographer, can see the subject, and are supposed to realize this. The reflective light meter will try to make everything average out to about middle gray. "Average" or "typical" subjects generally have wide tonal ranges which do in fact average out to about middle gray. If your subject is a more typical one, with typical wide range, and it actually does average out about middle gray, then great, easy as pie. If not an "average" subject, then you better pay attention, and stand ready to help with Flash Compensation or Exposure Compensation.
So reflected meters (for example, camera meters) only have this one way they can work. They are a dumb silicon chip, without any human brain. The meter has absolutely zero recognition about what the subject is, and has zero knowledge how it ought to look. Black cat in a coal mine, or polar bear in the snow storm? The meter has absolutely no clue what it is. The meter does not know if the subject is black and ought to be dark, or if it is white and ought to be bright. The human brain probably recognizes it instantly (in its surroundings), but the meter has no clue.... it simply sees some light. It can measure that light accurately, but it has absolutely no clue what it is, or what it means. Its best try is going to come out middle tone, which is a good compromise, considering. It is good that we realize this.
Handheld "incident" meters also exist, which stand at the subject's position, and aim back at the camera, and directly read the incident light falling on the subject, totally independent of the color of the subject (next page). These are less convenient to use (except in studio), but are greatly more consistent (accurate).
Bottom line: When the exposure does not come out right, it cannot help to cuss the meter or bemoan your fate. This is simply how meters work, and have always worked. The way we learn to use them is to study the picture, and figure out what the meter was metering to cause that middle tone result... why it happened? (usually, dark or light colored subjects or backgrounds are expected to cause mid-tone results). Then we learn to recognize those situations, and then we easily just know ahead of time what to do to prevent it next time we see a similar situation . There is no other way but to learn.
I say Flash a lot, but do not misunderstand - Metering in daylight works exactly the same way (middle gray result). But flash does seem more fussy about it (more on next page). The rapid falloff with inverse square law emphasizes differences (affecting flash, but not sunlight). And of course, the TTL preflash creates dark background shadows, metered as dark areas, which reduces the bright area that reflects and is metered. Flash is a little different.
Here is an old but good Kodak Tech article: Accurate Exposure With Your Meter. Still very true and valid and fully applicable in every way. All of this has been well known for many decades, metering has always worked this way. Good info, simply about how things work, and you can believe it.