In general terms, a mediator or intermediary was a neutral party that assisted in negotiations and conflict resolution, the process being known as mediation. One such mediator was Riva of the planet Ramatis III. (TNG: "Loud As A Whisper")
In November of 2154, Earth mediators attempted to negotiate a longstanding trade dispute between Tellarites and Andorians. (ENT: "Babel One")
In 2339, Curzon Dax acted as a mediator with the United Federation of Planets during the Klaestron Civil War. (DS9: "Dax")
In 2367, Jean-Luc Picard was described as an "accomplished mediator" by K'mpec. (TNG: "Reunion")
In 2369, Benjamin Sisko declined to be a mediator between the Ennis and Nol-Ennis during their faked peace talks. (DS9: "Battle Lines")
The same year, Sisko served at request of the Bajoran Provisional Government as mediator between the two Bajoran factions Paqu and Navot. (DS9: "The Storyteller")