We started with the understanding that your in-camera meter uses "average luminance" (i.e. brightness) to determine what exposure settings to use. That meant the camera's meter measured the total amount of light coming in through the lens, and assumed this light was spread perfectly evenly throughout the frame. The meter then suggested exposure settings that would make this average amount of light come out a medium gray tone in the final image.
This IS how light meters started out, however photography has come a long way and we now have more than one "metering mode" that controls how the meter behaves. There are basically three standard metering modes: matrix, center-weighted and spot.
"Matrix metering" is the smart(-ish) metering mode that is standard for almost all modern cameras. I'm going to use "matrix metering" in this post, but this is technically the Nikon term. I believe Canon calls it "evaluative metering" and the generic may be "zone metering", but I learned on Nikons and therefore I'm rolling with "matrix".
Matrix metering divides the frame into several different "zones" and measures the light in each zone separately. It uses this information to try and "guess" what kind of scene you are shooting and make exposure recommendations that would be best for this type of scene. Before this week that's basically all I knew about it, but thanks to Ken Rockwell's website (google him) I learned a bit more.
Let's use our old example of a snowy pasture to show how matrix metering works. Let's say our composition consists mostly of a snowy field, with a couple clumps of dark trees on the left side and the bright sun in the upper-right corner of the frame. Matrix metering is smart enough to know that there is nothing brighter than the sun that it can reasonably expect to run into. So when it measures something as bright as the sun in the frame (i.e. which is always the sun itself) it pays special attention to that. Matrix metering also knows that direct sunlight is very consistent and always produces the same amount of light. So now, matrix metering will pick exposure values that are suitable for subjects lit directly by the sun, and we will get realistic tones in our image that match what we see with our eye. The sun will be pure white, the snow will be a pretty bright white, and the dark trees will be black. Good job matrix metering!
Matrix metering has a lot of other logic included that helps it make good decisions. It is good at measuring the brightest and darkest areas of an image and trying to distribute these tones within the dynamic range of the camera. This means it tried to keep the brightest areas bright, and the darkest areas dark and strike a compromise somewhere in the middle. Here's a good example of it doing that:
See how it picked exposure settings that kept the dark areas from being pure black and the white areas from being pure white? It did a decent job of retaining detail in both these areas, and this looks reasonably like the scene did in real life (I know, a picture of the leg of my couch, how interesting).
That being said, as smart as matrix metering is, it is definitely not perfect and can be fooled. Let's go back to the snowy pasture example and pretend it is an overcast day instead. The meter is not going to see anything bright or dark enough to give it a good idea of what you are shooting. So it goes back to being a normal light meter. Most of the frame is snow, so it's going to make that medium toned (i.e. gray). If there are enough dark trees in the frame, its going to take them in consideration too and maybe pick slightly brighter exposure settings. In this case the snow may be a slightly lighter gray, but still not the white we are looking for. Sorry matrix metering, we know you tried.
Final thought: matrix metering is a good way to go most of the time for decent pictures. Its fairly smart and makes a lot of reasonable decisions. The problem is it still a machine, not a mind reader, and doesn't know your creative intent. Another problem is that it is not very predictable. If you are trying to over or underexpose something, its hard to know what the meter is already doing. Maybe it knows to overexpose the scene already (like the sunny snow day), or maybe it is hopelessly lost and shooting for a compromise (the cloudy snow day). If you are making your own adjustments, you have to guess how the meter already feels about this scene, which can be a mess.
That's the complex world of matrix metering, now let's move on to center-weighted and spot metering, which are much simpler!
