My friend, the late John Stanton, music hall historian, said that it meant 'private rooms for gentlemen' and I found this convincing. The earliest music halls (c 1840s to 60s), which had more of the character of barrooms than theatres, were normally attached to pubs, which had often acquired adjoining houses so as to build a big supper-room style hall across the united back land.
This meant that the front building tended to be an agglomeration of linked houses with a warren of rooms and passages. The publican had plenty of scope to let rooms for private functions, masonics and so on - and to provide... 'private rooms for gentlemen' where a music hall patron with coin to spare could retire with a companion for a quiet meal tete-a-tete, with reasonable certainty that there would be no interruption while the peace was preserved.
Arrangements of this kind have led to a common supposition that most early music halls were thinly disguised brothels. They were not. Prostitutes were evident in all music halls and some of the earliest of them certainly had friendly arrangements with neighbouring knocking shops, but no proprietor who had spent a great deal of money in building a hall, employing staff and engaging stage talent would have imperilled his licence by going down this path. 'Private rooms for gentlemen' may have been places of assignation and no doubt many an item of clothing was disturbed after supper, but the key word was 'private'.