Psychometry is a form of extra-sensory perception (i.e. magic) by which someone can gain information or memories about another person by touching objects associated with them. In IF, this generally means that when the PC touches a significant object they experience a flashback, either of their own memories (see amnesia) or of another character's.
The device is common both in IF and in graphic adventure. It has the advantage of allowing replayable flashbacks, and is well-suited to the object-based IF environment.