In theatre, a stage manager is in charge of what happens on the stage and in the back stage area. The house manager, or front-of-house manager, is responsible for everything else. This includes ushers, concessions, ticket booth workers and others. They are responsible for the safety and comfort of the audience and coordinate with the stage manager to ensure that the stage crew is aware of anything important going on in the front of the house and vice versa.
The primary duty of the front-of-house manager is to recruit, hire, train and schedule staff. For many small, community theatres this may be more difficult than it sounds as they are usually staffed by volunteers. Training means that staff should be aware of all of their duties and all of the procedures to be followed including dress codes. As a live medium, a theatre is reliant on everyone knowing how to do their job, even when things don't go as expected.
Generally, after the doors open and the audience begins filing in the only communication between the front-of-house and the back-of-house is between the house manager and the stage manager. The house manager will typically coordinate the opening of the doors and intermission. Beyond those things though, the less communication there is the better things have gone. The stage manager and house manager will typically only talk if something has gone wrong. None of the other staff will typically talk to the stage manager or anyone else in the cast and crew during a performance.
While the performance is ongoing, the front-of-house manager acts as a sort of host, while simultaneously managing several retail operations. The house manager is in charge of ushers, the ticket booth, concession stands, food service and the car park and valets. Hopefully the staff will be well trained and the manager will have reliable people at each station but if there is any problem with any of the stations, any of the staff or any member of the audience it falls to the house manager.
The ultimate responsibility of the house manager is the audience. The staff are all there to help but, over the course of an evening the house manager may need to intervene in any number of problems that arise from guests of the theatre. If an audience member asks to speak to "the manager" there is only one. The house manager also must be aware of any emergency contingency plans for fires, natural disaster and other disasters.