In modern usage, tar baby refers to any "sticky situation" that is only aggravated by additional involvement with it.
In one tale, Br'er Fox constructs a doll out of a lump of tar and dresses it with some clothes. When Br'er Rabbit comes along, he addresses the tar "baby" amiably, but receives no response. Br'er Rabbit becomes offended by what he perceives as the tar baby's lack of manners, punches it and, in doing so, becomes stuck. The more Br'er Rabbit punches and kicks the tar baby out of rage, the worse he gets stuck.
Now that Br'er Rabbit is stuck, Br'er Fox ponders how to dispose of him. The helpless but cunning Br'er Rabbit pleads, "Do anything you want with me --- roas' me, hang me, skin me, drown me --- but please, Br'er Fox, don't fling me in dat brier-patch," prompting the sadistic Br'er Fox to do exactly that because he gullibly believes it will inflict the maximum pain on Br'er Rabbit. As rabbits are at home in thickets, however, the resourceful Br'er Rabbit escapes.
Variations on the tar-baby legend are found in the folklore of more than one culture. In the Journal of American Folklore, Aurelio M. Espinosa examined 267 versions of the tar-baby story. The next year, Archer Taylor added a list of tarbaby stories from more sources around the world, citing scholarly claims of its earliest origins in India and Iran. Espinosa later published documentation on tarbaby stories from a variety of language communities around the world.