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. One who was simply born in a place, without regards to citizenship, was referred to as a native.
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)
After it became clear that the Romulan sun would go supernova, the Federation devised a plan to relocate 900 million Romulan citizens to worlds outside the blast of the supernova. (PIC: "Remembrance")