What does a theatre box office manager do?

A marketing manager for theatre manages all of the coordination for press, ads (radio, tv, & print), coordination of graphic design, programs, marketing materials (like a brochure with all the information about the plays in it). Also, they often manage the website for the theatre as it is also a marketing tool. That is just a general answer and often it will depend more on what the specific theatre will delegate to the Marketing Manager.