A weak or vulnerable factor.
The legend of Achilles has it that he was dipped into the river Styx by his mother Thetis in order to make him invulnerable. His heel wasn't covered by the water and he was later killed by an arrow wound to his heel.
Although the legend is ancient, the phrase wasn't picked up in English until the 19th century. It is used as a metaphor for vulnerability, as in this early citation, an essay by Samuel Taylor Coleridge in The Friend; a literary, moral and political weekly paper, 1810:
"Ireland, that vulnerable heel of the British Achilles!"
See also, the Samuel Taylor Coleridge phrase - suspension of disbelief.