Bracketing is the technique of shooting two or more images as different settings. This could be White Balance, for example, but is most often applied to exposure. Typically, a camera will shoot three shots when bracketing is applied – though some cameras can bracket three, five, even nine shots. You can often adjust the exposure spread too, either to reduce the variation of exposure, or to increase it. The latter is particularly useful when contrast is high, or you want to create an HDR in post-production. (See below.)
When bracketing exposure generally shoots the first shot at the ‘correct’ exposure, one shot underexposed, and one shot overexposed. (The first shot is based on the current exposure settings. If exposure compensation has been applied, then this will be the starting point for the bracketed sequence.) With bracketing set, you either press the shutter button three times, or use self-timer so that the camera shoots the three shots automatically.

Bracketing is a good safety net if you are not entirely sure what the most pleasing exposure should be. (You could then delete the unwanted images after you have decided.) The only drawback to shooting three images every time is that your camera’s memory card will rapidly fill up!