means A building or space designed for live dramatic performances, or by extension the art and profession of staging plays, or any room arranged for an audience (a lecture theater, an operating theater).

from From Greek 'theatron,' literally 'a place for viewing,' built from 'theasthai' — to behold, to gaze at — the same root that watches over 'theory' and 'theorem.' It traveled through Latin 'theatrum' into Old French 'theatre' before settling into English, carrying its original sense intact: not where actors act, but where watchers watch. The spelling split — 'theatre' versus 'theater' — is a much later Atlantic quarrel, with the '-er' ending favored in American usage.