This disorder is characterized by the presence of non-bizarre delusions which have persisted for at least one month. Non-bizarre delusions typically are beliefs of something occurring in a person's life which is not out of the realm of possibility. For example, the person may believe their significant other is cheating on them, that someone close to them is about to die, a friend is really a government agent, etc. All of these situations could be true or possible, but the person suffering from this disorder knows them not to be (e.g., through fact-checking, third-person confirmation, etc.).
People who have this disorder generally don't experience a marked impairment in their daily functioning in a social, occupational or other important setting. Outward behavior is not noticeably bizarre or objectively characterized as out-of-the-ordinary.
The delusions can not be better accounted for by another disorder, such as schizophrenia, which is also characterized by delusions (which are bizarre). The delusions also cannot be better accounted for by a mood disorder, if the mood disturbances have been relatively brief.
Criteria summarized from:
American Psychiatric Association. (1994). Diagnostic and statistical manual of mental disorders, fourth edition. Washington, DC: American Psychiatric Association.