There are several different opinions on correct usage of Theater vs Theatre:
1) One goes to a theatre to see a play, and to a theater to see a film.
2) The theater is the building and the theatre is the artistic performance on stage.
3) It's the same as the use of color vs colour. There is no difference in meaning, it's simply a matter of Americans spell it Theater while other parts of the English speaking world spell it Theatre. Americans use the spelling Theatre just to sound fancy.
4) In British English Theatre is the only spelling used and it indicates the art on stage and the building you view a play in. In British English you watch a film in a cinema never a Theater or Theatre.
Historically both spellings have been used. The word originated in Latin as "- re" but turned to "-er" in English use. Shakespeare actually used the spelling theater. In the mid 1600's the French spelling of "- re" began to influence England and British English standardized on the - re spelling while American English, not influenced by the French stayed with "- er".