Performing even a simple movement is a rather complicated process. First, the brain has to signal its intent to perform an action, which then gets translated into the specific motions that are required to achieve that intention. Those motions require a series of muscle contractions; the signals for these need to be sent out of the brain, through the spinal cord, and to the appropriate destination.
For most people who suffer from paralysis, it's really these later steps that are affected—most of the setup can still go on in the brain, but damage keeps the signals from making their way to the muscles. If there were a way to eavesdrop on the brain, it might be possible to identify an individual's intent and translate that into some form of useful action.
This may sound like science fiction, but significant progress has been made in the area. As far back as 2006, researchers were already reporting that electrodes placed in a person's motor cortex would allow them to manipulate an on-screen object in a three-dimensional environment. More recently, monkeys with a similar implant were hooked up to a robotic arm, which they learned to use to perform some simple tasks.
