Achilles was a child of Thetis, one of the Nereids in Greek mythology, and Peleus, the King of Fthia in Thessaly.
When Peleus met Thetis, he was advised by the Centaur Chiron to seize her and keep a firm grip on her.In order to avoid him, Thetis changed her shape first into fire, then into water, and later on to a wild beast.
However, Peleus didn't loose his grip until she had returned into her original form.
So the couple married on Mount Pelion and the gods celebrated the wedding with great splendor.
Soon, Thetis gave birth to a child by Peleus, she wanted to make him immortal. So one night, and in secret from Peleus, she buried the child in
the fire to destroy the mortal element in its nature that came from its father and then rubbed it with ambrosia.
But Peleus kept a watch on her, and when he saw the child squirming in the fire, he shouted out and grabbed the kid who had only burned his lips and the ankle of his right foot.
The origin of the name "Achilles" derives from this story (A-Hilla = one who has no lips)
Thetis, frustrated in her purpose, abandoned her infant son and went back to the Nereids.
Peleus delivered the child to the Centaur Chiron, who took him in,
fed him on the entrails of lions and wild boars and the marrow of bears, and taught the child temperance,
resistance to evil passions and resistance to pain.
However, according to another myth, Thetis bathed Achilles in the water of the Styx, the river of Hades.
The water of Styx had the ability to make everything invulnerable. Nevertheless,
the heel by which Thetis held her child, did not get touched by the magic water and remained vulnerable.