When Achilles was a baby, it was foretold that he would die in battle from an arrow. Naturally, his mother Thetis did not want her son to die. So she took Achilles to the River Styx which was supposed to offer powers of invincibility and dipped his body into the water. But as Thetis had held Achilles by the heel, his heel was not washed over by the water of the magical river. Achilles grew up to be a man of war who survived many great battles. But one day, an arrow shot at him was lodged in his heel, killing him instantly.
I had heard Achilles heel several times but never knew what it was about.