To expand on Gary's answer. Often, "citing" or "to give a citation" can mean "to name the specific rule, law, or piece of text that is the authority for your action." For example: "When asked why he could not support the law, the congressman cited the First Amendment to the U.S. constitution." In a formal academic paper, the footnotes or inline references that give the source for something are called citations. "According to Lord Rayleigh (1871, Phil. Mag. 4:41 pp. 107-120), the sky is blue because of scattering of longer wavelengths." Here, the date and page numbers are the "citation."
More generally, it can mean "explaining the reason or authority for your action."