I'll drop my two cents as well.
You half press the shutter, the camera takes a meter reading. If the line is to the left of the meter, you are under exposed. So you have to let more light in to get a well exposed image.
I definitely do not want to contradict Bigtwinky, who sure knows about exposure a lot more than I do, but this not necessarily true. This is only true if what you're shooting is a gray surface.
Try to use spot metering, Av exposure, manual focus set completely out of focus, and shoot a white sheet of paper. Then do the same with a black sheet of paper. In the pictures they will look the same color, a grayish sheet of paper.
This is because a white sheet of paper reflects a lot more light and the camera thinks that there is more light. A black sheet of paper reflects very little and the camera thinks you're in a really dark place and uses longer times.
Exposure meters are designed to set the exposure in such a way that the picture is a very well defined shade of gray.
Now, suppose that you're shooting in M mode. You have a white sheet of paper in front of you and you're still using spot metering. If you want it to be white in the picture, you need to set time and aperture (and ISOs of course) so that the indicator in the viewfinder reads an overexposure of 1 to 3 stops (depending on the type of paper, the dynamic range of the sensor or the film, whether it directly reflects light, etc... An opaque sheet of paper with a Nikon camera will look realistically white at about +1.5).
Suppose that you're shooting a black handbag. In order to make it black, you need to read about -2 or -3, depending on how reflective the handbag is.
Spot metering can be used either to make sure a single part of the photo is well exposed and who cares of the rest, or to "explore" the whole scene and make sure that all the different colors and brightnesses of the surfaces you're shooting are well rendered.
Another "exposure bible" is Ansel Adams, "The Negative: Exposure and Development". You can also get a glimpse by reading:
Zone System - Wikipedia, the free encyclopedia
One last note: Nikon claims that the matrix metering looks at the whole picture, compares it with thousands of pictures in their database and calculates the right exposure based on the colors and shapes that you're shooting. Besides the fact that I don't know how they do (unless you use live view), it does not always work. For example, try this on a street: select matrix, Aperture priority. Shoot a photo of a white care passing by. Then wait for a black car to pass by in the exact same position as the white one was and shoot it from the exact same angle (well, not really "exact"... it's not that you need a tripod, but the light conditions must be identical). Then look at the color of the tarmac in the two photos and you'll see that it is different. Doesn't that suck?
I'm far from an expert, I learned all this few months ago and I'm still struggling to put it into practice. A good exercise is to:
1) Explore the scene with spot metering and decide the exposure that makes the whites white, the blacks black, etc...
2) Shoot
3) Switch to Aperture priority and Matrix metering
4) Shoot again
5) Compare: did the matrix decide the same exposure as you did? If not, which one of the two photos looks more like the real scene in front of you? The first times that you realize that your manual choice was better than matrix, you'll love it!