The cornucopia symbolizes plenty and abundance. It originally comes from Greek mythology, supposedly having its origin with the horn of the goat that nourished and fed Zeus when he was still a baby. Zeus accidentally broke off the goat's horn, which then developed magical nourishing properties and never went dry.
There are many versions of the cornucopia story. Another myth suggests that Hercules created the cornucopia while breaking off the horn of a river god during a fight.
Eventually the cornucopia became associated with other deities. For instance, because the horn is a vessel of nourishment, the cornucopia is a sign of Demeter, who is the goddess of the harvest, or Gaia, the Earth goddess. Because the cornucopia symbolized abundance, it is also associated with Pluto, the god of wealth. The prosperity of cornucopia also meant that it was associated with the goddess of luck, Fortuna.
In modern times, the cornucopia is a symbol of Thanksgiving and the harvest. It is often depicted as a basket in the shape of a horn and filled with fruits and vegetables. This symbol has special significance for the United States, and is seen in the yearly Thanksgiving celebration. It is also immortalized in many state flags.