In the AV mode the camera decides on the settings to achieve what it computes as the best exposure possibly subject to constraint on the maximum iso and on the shutter time.

This computation is made according, among other things, to the evaluation mode (that is: the camera will compute the "ideal" exposure based only on the central part of the image, or on a larger area, or on some other more sophisticated approach).

This often works wonders and in many situation is a great help which avoids to miss a shot only because you forgot that you were going from within or from without. But you can find some cases where your interpretation differs from the camera algorithm. Maybe you are shooting a dark scene and you really want to get a dark image (while instead the camera could try to expose as to achieve a lighter scene, e.g. by raising the shutter time).

So you can in this case tell to the camera: look, I really want that you under-expose this image with respect to what you would normally do, so that I can get the desired result. The same applies to over exposing of course.

Note that (often) you can only do this in the AV mode in a range of +/-2 stops. But you can also take notice of the "correct" exposure and then pass to the manual mode and "under"-expose or "over"-expose by manually changing the settings as desired. When I say "under" and "over" I am really meaning that the final judgement on the "correct" exposure is yours and depends on what you are shooting and what you want to capture.

The same reasoning applies to the Tv mode (where instead of deciding the aperture you fix the shutter time and the camera judges the best ISO and aperture settings).