The bookwriter is the member of a musical's writing team who creates the book -- the musical's plot, character development, and dramatic structure. Essentially, the bookwriter is the playwright of the musical. He or she works very closely in collaboration with the lyricist and composer to create an integrated piece of drama.
There's a common misconception that the bookwriter merely writes the dialogue; though the book does include the musical's spoken text, it is much more than that, defining and organizing the dramatic action of the entire piece, including action that is musicalized by the songwriter(s). Even "sung-through," "operatic," or "through-composed" musicals, where there is little, if any, spoken text, require as much contribution from a bookwriter as do musicals with extensive dialogue scenes.
The bookwriter is often also the musical's lyricist, composer, or director.