The Iliad never mentions Achilles' heel, or even shows his death
Homer's greatest warrior is never described as invulnerable, and his death happens offstage, outside the poem. The story of Thetis dipping baby Achilles in the Styx while gripping one heel is a later legend, first found in Statius's unfinished Achilleid from the first century AD. Nobody knows whether earlier Greeks told it.
In Greek myth Achilles was the son of the sea nymph Thetis and Peleus, king of Phthia and one of the Argonauts. He grew up alongside his companion Patroclus, was taught by the centaur Chiron, and in the Iliad commands the Myrmidons. His defining deed is killing the Trojan prince Hector outside Troy's walls. Other sources agree that Paris later killed him with an arrow near the end of the war.
His parents' marriage was itself engineered. Zeus and Poseidon both pursued Thetis until Prometheus warned of a prophecy that she would bear a son greater than his father, so the gods backed off and married her to a mortal. Another version has Thetis rebuffing Zeus out of loyalty to Hera, whereupon he decreed she would never wed an immortal. There are also rival stories of how she tried to make her son immortal: besides the Styx, one account has her coating him in ambrosia and holding him over fire to burn away his mortal parts, until Peleus interrupted and she left in fury.
The name itself may carry a hidden theme. One analysis combines Greek achos, grief, with laos, people or soldiers, giving roughly he whose people suffer, fitting a poem where grief recurs constantly. Gregory Nagy reads laos as a body of troops, so the name cuts both ways: fighting well, his men bring distress to the enemy; acting wrongly, they suffer it themselves. Other scholars, including Robert Beekes, suspect a pre-Greek loanword, and resemblance to river gods like Achelous has prompted speculation he began as a water deity. The name already appears on Linear B tablets.
He also collected epithets, among them Podarkes, swift-footed, and Pyrisous, saved from the fire. His legend survives in everyday language: an Achilles' heel is a fatal weakness in something otherwise strong, and the tendon above the heel bears his name.
Source: Achilles