The story goes that Achilles was the son of Peleus and the goddess Thetis. Hoping to make her son immortal, Thetis dipped Achilles in the water of the River Styx, but because she held him by the heel as he did so, his heel did not receive the protection that the water gave to the rest of his body. Achilles became a great warrior, and he survived until almost the end of the Trojan War but the Trojan prince Paris finally managed to shoot Achilles in the heel, and he died. Achilles' death is not found in Homer's Iliad which ends with the death and funeral rites for Hector, another of the Trojan princes and the leader of the Trojan army. You can find out more at Wikipedia.
