What does amphitheater or amphitheatre mean?
The definition of amphitheater and amphitheatre
Am`phi*the”a*ter, Am`phi*the”a*tre,, n.
Etym: [L. amphitheatrum, fr. Gr. amphithé\’83tre. See Theater.]

1 An oval or circular building with rising tiers of seats about an open space called the arena.

Note: The Romans first constructed amphitheaters for combats of gladiators and wild beasts.

2 Anything resembling an amphitheater in form; as, a level surrounded by rising slopes or hills, or a rising gallery in a theater.