1. A formal and legal termination of a relationship or a judicial proceeding, etc.; especially, the formal declaration that annuls a marriage.
2. A court procedure that dissolves a marriage and treats it as if it never happened.

The most common reason for anyone to want an annulment instead of a divorce is for religious reasons.

Annulments are usually rare since the advent of "no-fault divorce" but it may be obtained in most states in America for one of the following reasons: misrepresentation, concealment; for example, of an addiction or criminal record, and the refusal to consummate the marriage.

3. A mental process or mechanism by which unpleasant or painful ideas are abolished from the mind of a psychiatric patient.

Such patients render as nonexistent, certain specific events or ideas which have been painful or disagreeable to them.