Denebians are a humanoid race from the planet Deneb V, located in the Alpha Quadrant.
The Denebians purchased all rights to a Vulcan fuel synthesizer from the con artist Harry Mudd in 2267. The Denebians contacted the Vulcans and discovered the deal was a fraud, and Mudd was arrested. He was given the choice of several forms of capital punishment, but since none appealed to him he escaped. (TOS: "I, Mudd")
Background
It has never been established in canon whether Deneb V is their homeworld, or whether they are offshoots of the Human or some other race.
It seems likely the Denebians are familiar with the telepathic humanoids of Deneb IV also mentioned in TOS. However, the Denebians obviously lack telepathic capability, or they wouldn't have been so easily tricked by Mudd.
It also seems unlikely the Denebians are related to the Bandi of Deneb IV, or that Deneb V is orbiting the same star as Deneb IV in TNG: "Encounter at Farpoint", since settling the actual star system around Deneb (Alpha Cygni) stated a major leap for the Federation into deep space in this TNG-episode, taking place ca. 100 years after "I, Mudd".