The Exposure Compensation button is one of the most useful features of a digital camera. Exposure compensation is a quick simple way to tweak exposure whilst in auto mode, shutter priority or aperture priority.
There are times when your camera's light meter will be confused by extremes of brightness or darkness - like photographing snow, something white on white or at night. It's because the camera thinks the world is mid grey.
So if you think the image in the camera's LCD looks too bright or too dark you can use the camera's exposure compensation to quickly and easily re-shoot the photo.
You can use exposure compensation to brighten or darken an image just by pressing the exposure compensation button and dialling in + or - exposure. On most DSLR cameras it's a little button diagonally split half white half black with + and - symbols on it. On some cameras you may need to search in a menu.
Best bet is to search the index of your camera's hand book for exposure compensation and it'll tell you where to find it.