These are variant spellings of a word derived from a Greek term meaning "to watch," "to look at." Theater is much the more common spelling, although some writers and some persons in theatrical professions seem to feel that theatre has more appeal and dignity: "Let's go to the theater (theatre)." "Medical students spend much time in the operating theater (theatre)." "The theater (theatre) of war stretched across the entire eastern half of the country."
Dictionary of problem words and expressions. Harry Shaw. 1975.