The term derives from a type of drama that was popular at the time of Boas' writing. It was most associated with the Norwegian playwright Henrik Ibsen. In these problem plays the situation faced by the protagonist is put forward by the author as a representative instance of a contemporary social problem. For Boas this modern form of drama provided a useful model with which to study works by Shakespeare that had previously seemed to be uneasily situated between the comic and the tragic, though nominally the three plays identified by Boas are all comedies. For Boas, Shakespeare's "problem plays" set out to explore specific moral dilemmas and social problems through their central characters.
The problem plays are linked by their characterised by their complex and ambiguous tone, which shifts violently between dark, psychological drama and more straightforward comic material; All's Well and Measure for Measure contain happy endings that seem awkwardly artificial and perfunctory, while Troilus ends with neither a tragic death, nor a happy ending. Boas used the term for plays in which the resolution of the themes and debates seems inadequate, and in the final act the deliverance of justice and completion one expects does not occur. Other definitions have followed, but all center on the fact that the plays cannot be easily assigned to the traditional categories of comedy or tragedy. The three plays are also referred to as the dark comedies, since despite ending on a generally happy note for the characters concerned, the darker, more profound issues raised cannot be fully resolved or ignored.
Many critics have suggested that this sequence of plays marked a psychological turning point for Shakespeare, during which he lost interest in the romantic comedies he had specialized in and turned towards the darker worlds of Hamlet, Othello, King Lear and Macbeth.
Some scholars regard Hamlet, which was probably written at the same time as Boas' original three "problem" comedies, to be a problem play as well. The term can also be applied to other odd plays from various points in his career, as the term has always been somewhat vaguely defined.