A special envoy or special emissary was a diplomatic rank that was given a very specific mission.
In 2293, Captain Spock was given the duties of "Federation Special Envoy" to the Klingon Empire, whereupon he conducted communications with Chancellor Gorkon. (Star Trek VI: The Undiscovered Country)
The half-Klingon K'Ehleyr was once granted the title while inside Federation space. Starfleet honored the moniker, because they viewed her as vital to the success of a mission regarding Klingons who still believed the Federation-Klingon War was raging.
Though defining the title was difficult, the power-relationship between K'Ehleyr and Jean-Luc Picard was one of rough equality. He was obliged to put USS Enterprise-D at her disposal, and to let her lead the response to the situation. Nevertheless, he still had a say in the precise manner in which the mission was carried out. In particular, she had initially thought the mission would require Enterprise to simply kill the under-informed Klingons, but he successfully insisted on a change of tack. (TNG: "The Emissary")
Ilon Tandro was a special envoy from Klaestron IV who was in charge of the extradition procedure of Jadzia Dax. (DS9: "Dax")
In 2399, Raffi Musiker convinced Captain Emmy Bosch to have Jean-Luc Picard designated a Federation special envoy to the Borg Reclamation Project, so that the Romulans would grant his request to meet with the Project's executive director Hugh. (PIC: "The Impossible Box")