Citizenship was one's status of belonging to or living in a particular city, country, planet, or group of planets. This afforded them certain benefits. An individual who had citizenship was known as a citizen or as a national.
Federation citizens were entitled to the protection of the Federation. In 2269, Captain James T. Kirk refused Koloth's demand that Cyrano Jones be handed over to him, citing Jones' citizenship as the reason for being unable to comply. (TAS: "More Tribbles, More Troubles")
In 2293, following the capture of Kirk and Leonard McCoy by the Klingons, Admiral Cartwright protested that Starfleet could not just sit by and allow Federation citizens to be abducted. (Star Trek VI: The Undiscovered Country)