Bracketing is the technique of taking several shots of the same scene using slightly different settings. This can be achieved manually, or by using in-camera automatic bracketing features, such as AEB (Auto Exposure Bracketing) and FEB (Flash Exposure Bracketing).
A Little More Detail:
The practice of bracketing usually refers to exposure bracketing, whereby one scene is photographed in a series of underexposed through to over exposed shots. However, it can also apply to other photographic parameters such as White Balance.
Bracketing is commonly used to enable the photographer to choose one image from a series of shots that they are the most happy with.
Alternatively, all the images in a sequence can be composited in to one image, using post production software, such as Adobe Photoshop. This is often referred to as High Dynamic Range (HDR) editing.