The voice coach (aka: collaborative pianist) is the person who deals with the musical, language and dramatic demands of the vocal repertoire. They are pianists who have done training in diction, repertoire, collaborative piano and opera. The goal of the vocal coach is to serve as the other half of the music (piano part or orchestra reduction) and help the singing put everything together. They expect a singer to arrive with notes learned, language translated, and an idea about how the song should be presented. From there the coach is the musical "mirror" for the singer and reflects back what they hear and makes suggestions on how to make any necessary changes.
I like the mirror comparison a lot, which I had never considered. I've also previously written about the difference between voice teacher and coach.