What the heck is playback?
 

I've been hired to do sound for a music video. (There's apparently dialog they want to get.) I was told that one of my responsibilities is "playback." Is this a standard term? I've never heard this before. The producer seemed a little unclear on what this would entail. It does seem to include playing music for people to lip sync to. Is there more to it than that? Anything I need to know? I've never done a music video before.

It is indeed playing music on the set for performers to sync or to dance to. Depending on the situation its setup can range from the fairly simple to quite complex. Wolf Seeberg has a good overview of what may be required in his "Sync Sound" book.

As Steve said, this can range from simply playing back a CD into an amplified speaker, up to fully timecoded recorders/players and cameras.
You should definitely meet with the technical people who are responsible for their music production and the camera crew and iron out those details.
On simple, non-timecode shoots, a CD is prepared that has the whole song, major portions of the song, and smaller important bits of the song that are likely to be shot many times in a row, all on separate tracks with a lead-in beat. Then it's up to the director to call for starting and stopping the playback of the appropriate track into a speaker system that's loud enough for good sync performance. For a rock video, you'll need to play loud enough for the drummer to hear over his real drumming. I usually wear hearing protection that still allows me to hear the director.
Guide audio is recorded on the cameras and the editor has their hands full organizing and syncing all the parts.
If dialogue is being recorded, this is usually done during silence after a lead-in beat and people are expected to stay in sync on their own for short periods. For longer periods of dialogue a very low frequency thumper track is played back for people to maintain sync. This can be mostly eliminated with a low cut and the rest is masked by the final music mix.

Excellent. Thanks Jay and Steve. Man, those were quick responses.