Any place rising by steps like the seats of a theater.
Usage notes
The spelling theatre is the main spelling in British English, with theater being rare.
In United States English, theater accounts for about 80 percent of usage in the major corpus of usage, COCA.
Among American theatre professionals, there is some usage of the two spellings in order to differentiate between the location theater (as in definitions 1-5) and the art-form theatre (definition 6). A variant of this differentiation is the usage of theatre for things relating to live performances (as in definitions 1 and 6) with theater being used for all other uses.