Achilles died during the Trojan War after being shot in his one vulnerable spot—the back of his heel—by a poisoned arrow. The arrow was shot by Paris, the Trojan prince, and in many versions of the myth, the god Apollo guided the arrow to that exact spot. Achilles' mother, Thetis, had dipped him in the River Styx to make him nearly invulnerable, but she held him by his heel, which was not immersed and thus remained vulnerable. This small weakness ultimately led to his death when Paris' poisoned arrow struck it, causing fatal injury during battle or in some accounts, as he was about to sack Troy or negotiate peace. After his death, Achilles was cremated and honored among the heroes.
Anatomically, the Achilles tendon is very strong, but an arrow wound there, especially with poison, could cause lethal effects either through poisoning or arterial damage leading to fatal bleeding.