A Doll's House by Henrik Ibsen is a prime example of a problem play in that it deals with social issues and exposes social evils. This largely explains why it was so controversial in its day. Most people who went to the theater in nineteenth-century Europe did so because they wanted to be entertained. They most certainly didn't go because they wanted to be confronted with social problems.
But Ibsen, a staunch proponent of naturalism in drama, believed that it was important to use theater as a vehicle for depicting the realities of contemporary society, no matter how uncomfortable they might make people feel. It was only by dealing frankly and openly with what was actually happening in society that any kind of social change was possible.
The problem addressed by Ibsen in A Doll's House is female oppression. The central character of Nora Helmer lives in a world in which women are treated as second-class citizens. Lacking the same rights and opportunities as men, they are marginalized, infantilized, and kept in a state of permanent subjection by their menfolk.
The appalling treatment of women in nineteenth-century European society is epitomized by the marriage between Nora and her husband, Torvald. Torvald treats Nora like a child, someone who lacks the requisite agency to make her own decisions in life.
For him, as for most men in his society, women are to be confined to the home, where they are to raise children and do the housework. The world outside, the world of business and public affairs, is the exclusive domain of men, from which women are excluded for what is allegedly their own good. Among other things, this prevents, as it is supposed to do, women from becoming independent and making their own decisions in life.
Eventually, Nora solves the problem of female repression by leaving her husband and children and venturing out into the big wide world. But the nature of patriarchal society ensures that her life outside the respectable middle-class home will be something of a struggle. And so the problem with which Ibsen deals remains one that will still need to be dealt with in subsequent plays.