A single-celled organism was a lifeform which consisted of a single cell. This contrasted with a multicellular organism. Single-celled organisms were typically microorganisms.
In 2268, for lack of a better term, a space amoeba encountered by the crew of the USS Enterprise was described as a giant single-celled animal. (TOS: "The Immunity Syndrome")
According to Doctor Beverly Crusher in 2364, cell division in single-celled lifeforms, at least organic ones, was preceded by a resting state. (TNG: "Home Soil")
In 2373, Captain Kathryn Janeway sarcastically stated it was flattering that Q chose her to be his mate over a single-celled organism after he mentioned he could have also chosen a Cyrillian microbe. (VOY: "The Q and the Grey")