Dramaturgy is the process and art of writing and staging a play. Your little brother's preschool production of "The Three Little Pigs" might not be an example of excellent dramaturgy, but it is adorable.
Playwrights, theater directors, and drama teachers are the most likely to throw around the term dramaturgy. It encompasses everything that's involved in creating a play and producing it on an actual stage for an audience to watch. Dramaturgy is especially focused on the play's setting, social context, political themes, and the psychology of its characters. The word itself comes from Greek roots drama and ergon, "work or activity."