The basic idea behind BCIs is to enhance cognitive capabilities. An average computer is able to perform any particular operation up to 20.000 times quicker than the human brain, which needs time in the region of whole milliseconds for processing one bit of information. A brain-computer-system -some people would call it a cyborg - thus could be a worthwhile symbiosis when it comes to storage and retrieval of information or speed and precision of actions. Some fancy things also can be done with thought-controlled computer games. You can see the first steps towards this huge market on the pictures on this side, starring tennis-player and cube-rotators...
The most promising application of BCIs, though, is with patients that are for a medical reasons unable to use their bodies for everyday purposes. This is especially true for patients suffering from neurological conditions like amyotrophic lateral sclerosis (more), brainstem stroke (more), cerebral palsy (more) or muscular dystrophies (more), but also for victims of accidents with brain or spinal cord injuries. These patients could eventually learn to control a prosthesis only by thought.