This article is from the Bipolar Disorder FAQ, by firstname.lastname@example.org (Barry Campbell) with numerous contributions by others.
Delusions are, in general, "false beliefs." The DSM-IV (p. 763) defines a
A false belief based on incorrect inference about external
reality that is firmly sustained despite what almost
everyone else believes and despite what constitutes
incontrovertible and obvious proof or evidence to the
People who are in a manic or depressed episode may have delusions. Some of
these might include delusions of reference, where the individual feels like
events, objects, or other persons have a particular and unusual significance.
The individual may also have grandiose delusions or delusions of persecution
(such as paranoia).
It's important to note that delusions must be diagnosed in terms of
cultural, social, and religious norms. A belief that one is in direct
communication with God, for example, might be either a delusion or an
expression of certain kinds of religious faith. :-)