What is a bracketing button for on a DSLR?

There are two types of bracketing: auto exposure bracketing and white balance bracketing.

Auto exposure bracketing makes the camera take three (or more if you shoot Nikon) images in rapid succession. Each of the images will capture a different exposure. The first shot will be neutral exposure, the next shot will be a lower exposure (darker) and the last picture will be brighter. This helps if you're in a situation where you're not sure what the correct exposure would be. Also, it is used in HDR imagery.

White balance bracketing does the same thing except you are bracketing the white balance with each shot. This is useless if you shoot in RAW because you can simply change this afterWord.