A cultural observer was someone tasked with the anthropological study of a civilization. A cultural observer normally minimized the amount of influence they themselves made on the civilization being studied, and often worked as part of an observer team to study different aspects at the same time.
The United Federation of Planets employed cultural observers in pre-warp civilizations for research and assessment. In accordance with the Prime Directive of non-interference, the research was strictly covert. After the late 23rd century, covert cultural observers became a required preparatory step to first contact. (Star Trek: Insurrection; TNG: "First Contact")