Far from being plays with fatal flaws, as one might imagine from the name, problem plays are actually plays which are designed to confront viewers with modern social problems. Typically, the theme of the play is socially relevant, and the characters confront the issue in a variety of ways, presenting viewers with different approaches and opinions. After seeing a problem play, one is supposed to be filled with interest in the topic at hand, and hopefully inspired to enact social change.
The concept of problem plays arose in the 19th century, as part of an overall movement known as Realism. Prior to the 19th century, many people turned to art as a mode of escape which allowed them to look outside the world they lived in. In the 19th century, however, art began to take on a more introspective, realistic air, with a conscious focus on ongoing issues such as the social inequalities exacerbated by the Industrial Revolution.
Although the idea of creating problem plays was popularized in the 19th century, numerous works have been retroactively termed problem plays. Several Greek playwrights, for example, addressed ongoing social issues like war, in the case of Lysistrata, by Aristophanes. Several works of Shakespeare are also considered to be problem plays, like Measure for Measure, which has very Biblical themes of justice and truth, or Troilus and Cressida, which confronts viewers with infidelity, sexuality, and betrayal.
Many people regard Henrik Ibsen as a master of the problem play, along with authors like George Bernard Shaw and some 19th century French playwrights, many of whom were also authors. Problem plays can cover a wide variety of topics, ranging from women's rights to greed and inequality, and they can tell their stories in a wide variety of ways. For example, it is common to have a tragic protagonist who ultimately suffers as a result of his or her refusal to confront social problems.
Essentially, problem plays are a form of commentary on the societies they are performed in. Because social problems are often universal across cultures and eras, many people find something to appreciate in problem plays, whether they are contemporary or not, and such plays tend to be popular in performance. They can also be difficult to watch, as many people find something of themselves in the characters, and struggle with this revelation.