An Achilles' heel is a specific weakness or vulnerability that might lead to failure. An otherwise excellent basketball player might consider her Achilles' heel to be the fact that she's short.
In Greek mythology, Achilles was protected from a curse by being immersed in magical water as a baby. His mother held his heel as she dipped him, leaving it unwashed by the protective water. His Achilles' heel was literally his heel, the one part of him vulnerable to the poison arrow which eventually killed him. Your Achilles' heel might be your lack of upper body strength, your laziness, or your shyness — anything that's a particular weak spot.