Achilles was a hero of the Trojan War and the main character in Homer's Epos, the "Iliad"
Achilles was the most handsome, capable and worthy of all the heroes who participated in the Trojan War.
Family of Achilles
Achilles was born in the ancient city of Fthia (presumably the modern Farsala of Thessaly/Central Greece) as the son of Peleus, the King of Fthia, and the silver footed sea goddess Thetis.
The character of Achilles
Achilles was a passionate, generous, brave hero but had also an impulsive and quick-tempered character. Many times he even gave the impression of being arrogant. During the Trojan War, Agamemnon accused Achilles for being a narrow-minded soldier who loved conflicts, wars and battles 
The weakness of Achilles
Thetis, the mother of Achilles, was strongly attached to her son and when he was born, she attempted to make him immortal by dipping him in the sacred waters of the river Styx. However, Thetis did not quite achieve what she had hoped for... while she was keeping him inside the waters, she had to hold her child by one heel, leaving one vulnerable spot in the body of Achilles. This weakness turned out to be crucial for Achilles, since he got killed during the Trojan War by an arrow that hit exactly that spot.
The expression "Achilles heel" remains until today, describing a small, but important weakness of a human being.
View the probable location of Ancient Fthia in a larger map