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")
Some time before 2383, a slave owner ran a show featuring enslaved performers staging theatrical battles in a large arena resembling medieval castle architecture. Audience members watched the performance from the shadows on top of the arena walls, looking down at the performers and out of immediate harm's way. (PRO: "Preludes")
In 2384, Enderprizians of the colony New Enda-Prize performed stage plays to pass down their colony's history, performances they called "playing the logs." They called their stage "the Bridge", and its backdrop resembled the bridge of a Constitution-class starship. They used movable scenery to dress the set to represent the USS Enterprise, the woods leading to "the Gallows", and the hero En Son's deathbed. (PRO: "All the World's a Stage")