Bracketing is a kind of exposure insurance. In tricky lighting conditions, the camera's meter can have problems getting the exposure just right. Instead of trying out just the one exposure, you can give multiple exposures (usually three but sometimes five) at different settings. Let's say you are in manual mode and you've chosen f5.6 @ 1/250th, you'd also give it one stop less exposure and one stop more (so you'd be changing either the shutter speed or the aperture..... in a digital camera you could actually also alter the ISO but this is less commonly done).
That's the manual way, and the various automatic modes can do the same, more easily.