P300 is the name of an electrical peak of about 300ms in lenghth. It occurs in the EEG when recorded over the so called parietal cortex, an area on both sides of the brain roughly some centimeters above the ears. The p300 peak is an unconscious reaction on significant or unusual auditory, visual or tactile stimuli.
To use it for a BCI, users face a matrix with numbers or letters, say 6x6. These rows or columns flash one after the other at a rate of about eight times a second. The user has to count how often the desired letter or number is illuminated, and doing so, he unconsciously produces p300 peaks (kind of an electrical "ahhhhhh"...), which the software averages to find out the user's intent (see illustration).
P300-based BCIs have a number of technical and practical advantages (more) and are likely to be considerably faster than the SCP-systems, but there has not yet been enough practical experience with them to give a final judgement.