Theatrical production management is a sub-division of stagecraft. The production management team (often consisting of a production manager and any number of assistants) is responsible for co-ordinating the various sub-diciplines (scenic, wardrobe, lighting, sound, &c.) of any large theatrical presentation, as well as overseeing the stage management team. In most professional theaters the production manager is the highest ranking person on the production staff and answers directing to the general manager and or/artistic director.
Production management also deals with the logistics of the production itself, e.g. the procurement of rehearsal space, the booking of the theatre, &c. The production manager's job is rather fluid, however, and may also include just about anything an enterprising producer or director may dream up. Usually, though, the production manager's job is mainly supervisory, although it requires excellent 'people skills' in order to smooth over disagreements that inevitably arise.