Once upon a time, the Chicago Tribune asked me that question

As a dramaturg, I work as an "information designer," keeper of text and context. 

Reminding of the production's original vision and anticipating the audiences to come, the dramaturg serves as a bridge between the two, providing contextual research and interpreting the play from its script, its cultural history, and its previous productions.  

Above is one of many lobby display panels I created with graphic designer James Keister for TimeLine Theatre, this one for Noel Coward's This Happy Breed. In addition to placing the audience in the era of the play, the display situated ten events from 1919-1939 that we as a production team chose to situate between scenes, with film collages of period footage and original music. From Hauptmann to The Lion in Winter to Guantanamo: Honor Bound to Defend Freedommy work with TimeLine exemplifies my dramaturgy outside of productions. The work inside the production can sometimes be a moving target

What else do dramaturgs do? Bridge between the cast/staff and the text, commission plays, plan seasons, organize related events, make multimedia pieces....