A federation was a political union of semi-autonomous states under a central government.
In 2259, R'ongovian diplomat Vasso L'Gaelia asked T'Pring, whose katra was secretly inside the body of Spock, "What is the logic of an alliance with a federation whose interdependence merely dilutes the cultures that comprise it?" T'Pring responded that as a Vulcan, she sympathized with Vasso's fears that they would lose their culture to homogenization in a multilateral alliance like the United Federation of Planets. (SNW: "Spock Amok")
In 2364, Lieutenant Commander Data described the Tkon Empire as a huge space federation which had been extinct for 600,000 years. (TNG: "The Last Outpost")
In 2366, Deanna Troi explained, during a first contact mission, to the Malcorian Dr. Mirasta Yale, that they were "from a federation of planets," before explaining that she was from a planet called Betazed, and Captain Picard was from another called Earth. (TNG: "First Contact")
When Torat, who lived in space controlled by the Devore Imperium, was contacted by the USS Voyager, which Captain Kathryn Janeway described as belonging to the Federation, commented, "Federations. Imperiums. Why do you people feel such a need to align yourselves with monolithic organizations?" (VOY: "Counterpoint")
In 3189, Minister Osyraa described the Emerald Chain as "a federation of mercantile exchanges" to Fleet Admiral Charles Vance. (DIS: "There Is A Tide...")