A stage was a raised platform on which actors and dancers could perform.
In 2266, while at a theater with James T. Kirk, Doctor Thomas Leighton identified "that man on the stage" as Kodos the Executioner (TOS: "The Conscience of the King")
Julian Bashir used to watch ballerina Palis Delon on stage, finding her dancing to be amazingly graceful. He related this to Miles O'Brien in 2370. (DS9: "Armageddon Game")