A psychiatric facility was a medical facility designed to treat patients for mental disorders that required more extensive treatment than available on an outpatient basis.
The colony on Benecia was noted for its first class psychiatric facilities. After killing her father and several other eyewitness survivors of the Tarsus IV Massacre, Lenore Karidian was committed to the psychiatric facilities there. Doctor Leonard McCoy informed USS Enterprise Captain James T. Kirk that she would receive the best of care there. (TOS episode: "The Conscience of the King").
The Mira Romaine Center for Rehabilitation and Reintegration was a type of psychiatric facility used to treat Federation citizens - especially Starfleet personnel - who had suffered mental possession or mind control by an alien influence. (TTN novel: Takedown)