Mrs. Warren's Profession by George Bernard Shaw is a prime example of the genre known as the problem play. This genre first developed on the Western stage in the late nineteenth century to cater to a growing awareness among the middle classes of certain problems within contemporary society.
Problem plays often dealt with highly contentious and controversial issues that had traditionally been avoided or ignored for fear of offending the delicate sensibilities of respectable theatergoers. One such issue, the one dealt with in Mrs. Warren's Profession, is prostitution. The title character is a prostitute and madam of a string of brothels who's made a lot of money from her many houses of ill repute.
Even so, despite her extraordinary wealth, she's a living, breathing testimony to the gross inequalities of Edwardian society, in which employment opportunities for women were extremely limited. What's more, Mrs. Warren's illicit profession has severely undermined her relationship with her daughter, Vivie, who, despite being an independent-minded young woman, ends up disowning her mother.
The social problem dealt with by the play, then, remains unsolved. That is because it is a structural problem that requires a radical, long-term change in society that will make it possible for women to make their own way in the world without having to resort to prostitution.