What is the meaning of an apple of discord?

The phrase "an Apple of discord" means a cause for dispute.

It is derived from a story in Greek Mythology.

A golden Apple was dropped before three Goddesses, Hera (Wife of the Chief God), Athena (Goddess of War), and Aphrodite (Goddess of Love and Beauty). On the Apple was a note saying something to the effect of "To the Fairest". Obviously, this caused an argument over which of the three was the most beautiful.

In order to solve the question of who was the fairest, the three Goddesses appeared before the young Trojan prince Paris, to ask him. They each bribed him, offering him a gift if he chose them. Paris chose Aphrodite, who told him he could have the most beautiful woman in all the world.

The most beautiful woman was Helen, wife to Menelaus. Paris and Helen fell in love, then ran away to Troy. This is what began the legendary Trojan war.