Horn of Plenty
The original cornucopia was one of the horns of the goat Amaltheia, which suckled the great god Zeus when he was an infant. Zeus was so grateful to Amaltheia (who apparently has some relationship to Pan) that he placed her in the heavens as the constellation Capricorn, but he took one of her horns as a present for the nymphs.
Zeus spent a great deal of his time on the seduction of nymphs, and it would appear that he used the first cornucopia as a tactic in overcoming their resistance. He told them that whenever they needed anything to eat or drink, they should ask the horn and it would overflow with everything they desired. The nymphs found that this promise by Zeus (unlike some of his other promises) was amply fulfilled. Whenever the nymphs asked the cornucopia for fruit, grain, honey, wine, or any other food or drink, the horn responded so bountifully that they could feast to their hearts' content.