Well, you surely know the story of Brer Rabbit and the tarbaby, right? Brer Fox and Brer Bear want to catch Brer Rabbit, so they make a dummy out of tar and set it out on the road. Brer Rabbit comes along and says hi, but the tarbaby says nothing. Brer Rabbit says hi again, and the tarbaby still says nothing. So Brer Rabbit gets pissed and gets in a fight with the tarbaby--getting hopelessly stuck and befouled by the tar.

So a tarbaby troll is a troll who antagonizes people until they smack him, which gives him a chance to smack back, and then you've got a fight that makes everyone look just as filthy and sticky as the tarbaby.

The lesson is: if you ignore the tarbaby, you won't have to worry about getting thrown into that briar patch...