The legend was that his goddess mother had, when he was a baby, dipped him in the Styx River to make him immune from death, however by holding him by the back of the ankle, that part was not dipped, and so that was his 'Achilles heel' which crafty Paris took advantage of with his arrow rather than a face to face fight which he was sure to lose. Hence the tendon has come into popular expressions as the Achilles tendon and the expression Achilles heel for someone's weakness.

Did you see the movie "Troy"? Keep your eye on Brad Pitt's character and how he dies.
The Achilles tendon is part of the heel. In Homer's the Illiad, Achilles is a Greek hero who, as a result of being dipped in the river Styx as an infant by his mother, was invincible and could only be harmed by striking his heel. At one point in the Trojan War, Paris lodges an arrow there, and Achilles is slain. The fact that it was his heel is the root of the name Achilles tendon, and the fact that that was his weakness is the root of the phrase "Achilles heel".
it got its name because Achilles the Greek warrior had an arrow go through his. This disabled him and the tendon has been given his name.