Psychoanalysis is the name of:
1) a procedure for the investigation of mental processes which are almost inaccessible in any other way, especially inner experiences such as thoughts, feelings, emotions, fantasies and dreams;
2) a method (based upon that investigation) for the treatment of neurotic disorders;
3) a systematic accumulation of a body of knowledge about the mind, obtained along these lines, which is gradually turning into a new scientific discipline.
For a more detailed explanation go to the Tampa Bay Psychoanalytic Society site.
Definition from the Encyclopedia Britannica.