1. To cite is to reference a statute or case to provide legal authority for a fact or legal proposition. For example, an attorney would probably cite Miranda v. Arizona, 384 U.S. 436 (1966), if he was arguing that his client had not been informed of his right to remain silent when he was arrested.
2. Cite is also used interchangeably with “citation,” for example, a judge might ask an attorney if he has a cite for the legal proposition he is arguing.
3. Finally, to cite is the act of issuing a citation to someone. For example, the police can cite a homeowner for keeping broken down trucks on his front lawn.