The story is almost formulaic, and reminds me strongly of the story of Sleeping Beauty - but instead of an evil fairy named Maleficent, the main character is the sinister Goddess of Discord and Strife: Eris.
Thetis, basically the most eligible bachelorette of the Gods (until it was prophesied that her son would be far greater than his father, and then kill his father), was marrying Peleus. Everyone who was ANYONE was invited, but Eris, Ares' annoying and dangerous sidekick, was left off the guest list. It wasn't any kind of accident - the Gods knew that Eris' love of mischief would totally ruin the wedding reception. But Eris showed up anyway, and she was PISSED! She had brought with her one of her beautiful and shiny Golden Apples. The shiny Apple of Discord. This was no wedding gift to the bride or groom.
Eris threw the apple into the room, between the three Goddesses Aphrodite, Hera, and Athena. On the beautiful apple was inscribed the simple words "to the fairest." All three fell to the charm of the apple's beauty and her own divine vanity - they all demanded the apple. When they couldn't reach a consensus (shocker!), they went to Zeus. Wow. Sucks to be him. He decided to delegate that question to someone else, because he knew that whichever Goddess was chosen, the other two were going to inflict some serious revenge.
The poor kid who was chosen for answering the question was Paris (also called Alexander). Sweet little Paris was just chilling on Mt. Ida, shepherding, because it had been prophesied that he would cause the Trojan War and Troy's downfall. Zeus descended and explained the situation, and then the three Goddesses came down in all their beauty and glory, and demanded the apple. Paris made a little choking noise and almost started crying. How could he, a mere mortal, decide which of the most beautiful women he would EVER see were the most gorgeous. He couldn't decide.
But he knew he had to make a decision. The Goddesses pretty much decided that for him. Each one offered him a gift, letting him give the apple to the one with the best gift.
Hera, the queen of the Gods, offered Paris power. She filled his head with images of thrones and conquering, and promised him that he should have all of Asia at his feet. Now, that sounded pretty damn good to Paris, but being a reasonably intelligent mortal - and very capitalistic - he decided to hear the others out and go with the highest bid. But he wasn't to get any more offers of power. Each of the Goddesses had her own domain, and her gifts corresponded appropriately. Athena went next. She offered him great wisdom, almost equalling her own, and promised him great luck in battle. She swore to make him the best strategist ever. Again, Paris was ALL about the idea, but he decided to wait and hear what Aphrodite had to say. That was the problem. Paris may have been smart, but he was a guy with normal hormones. Waiting to hear what the Goddess of Lust had to say pretty much screwed him over. Aphrodite told him two things: 1) that he would have the BEST body ever 2) that he could have the most beautiful woman in the world as his mate. And I have no doubt that she promised it in her most seductive voice painting visions of ecstacy in his mind. Paris decided to go with Aphrodite.
Here his wit failed him in more than one way. Helen of Troy was the most beautiful woman in the world - but she was already married, and married to an important king, no less. HE was already married to a nymph named Oenone. Oenone had learned the art of prophesy from Rhea, and forsaw a gruesome death for Paris should he try to take Helen. She begged him to stay, but Paris was entangled in the sexuality Aphrodite had left in his mind, and would not listen. In one more area did Paris' logic fail him. He had angered the Goddess of War and Wisdom and the Queen of the Gods who commanded power. He had no idea what he'd gotten himself into.
Paris did indeed steal Helen away - but not without cost. The theft/kidnapping/rape began the Trojan War - just as the prophesy at his birth had proclaimed. With Athena and Hera deadset against Troy, they were in for a run for their money. Troy eventually fell, and Paris was mortally wounded. His wife, Oenone, could have saved him - but she was so bitter from his betrayal that she refused. A few days later she changed her mind, but by then, it was too late, and when she found Paris dead, she hung herself.
That is the story of the Apple of Discord - don't mess with Eris.