The cornucopia, literally 'horn of plenty,' comes to the Thanksgiving table thanks to Greek mythology. The horn may have originally been that of a goat which the infant Zeus used to drink from. In the story of Zeus' childhood, it is told that he was sent away to a cave for safekeeping to prevent his father Cronus from eating him. Sometimes it is said that he was nursed by a goat named Amalthea and sometimes that he was fostered by a nymph of the same name who fed him on goat's milk. While an infant, Zeus did what other babies do -- cry. To cover up the noise and keep Cronus from finding out his wife's plot to protect her son, Amalthea asked the Kuretes or Korybantes to come to the cave in which Zeus was hidden and make lots of noise.
Evolution of the Cornucopia
There are various versions of the evolution of the cornucopia from a horn sitting on the head of the nurturing goat. One is that the goat tore it off herself to present it to Zeus; another that Zeus tore it off and gave it back to the Amalthea-goat promising her abundance; another, that it came from a river god's head.
The cornucopia is most frequently associated with the goddess of the harvest, Demeter, but is also associated with other gods, including the aspect of the Underworld god that is the god of wealth, Pluto, since the horn symbolizes abundance.