In Dianetics, an engram is defined as a painful memory which is embedded in the stimulus-response unconscious (the reactive mind) rather than as a normal memory. Through auditing, people can become “clear” of engrams.
At higher levels of Scientology (OT_III), it is revealed that engrams are the lost souls of the previous inhabitants of Earth (aka Teegeeack) who were killed, nuked AND brainwashed by the evil galactic warlord Xenu.