Theatre (British English and also American English), or Theater (mostly American English), has several meanings.
The word comes originally from the Greek Theatron, meaning roughly, 'a place for viewing'. In American English, the word 'theater' can mean either a place where films are shown (this is also called a cinema) or a place where live stage plays are performed. In British English, 'theatre' means a place where live plays are performed. Some people, both English and American, use the spelling 'theatre' to mean a place where live plays are performed, and the spelling 'theater' to mean a cinema.