1.nounAn open, outdoor theatre (which may be a theatre in the round, or have a stage with seating on only one side), especially one from the classical period of ancient Greece or Rome, or a modern venue of similar design.
"Ancient Roman amphitheatres were mostly oval or circular in plan, with seating tiers that surrounded the central performance area, like a modern open-air stadium."
2.nounA natural formation of a similar shape, where a steep mountain or slope a particular rock formation forms a partial or compete bowl, especially one used as a performance space (and possibly modified by carving out seats, etc) because the slopes naturally amplify or echo sound.