For electric guitarists, distortion refers to the clipping of a signal when it is (hopefully purposefully) amplified beyond the abilities of some component or another of his rig to handle it. The common favorite component to distort is a vacuum tube in the amp. There are other methods of generating distortion. Common myth is that The Kinks started the whole thing by putting a pencil through a speaker in the guitar rig.
See guitar amplifier for more information