How does the Binding of Isaac work as a story rather than a religious event?
The Binding of Isaac, called the Akedah in Hebrew, is an event during Isaac's life in the Old Testament during which his father's faith in God was tested.
Abraham and his wife Sarah had tried to conceive for years, but only after an angel visited their house did she have a son. God then tested Abraham by ordering him to offer Isaac up as a sacrifice. Abraham carried out the order, all but the actual sacrifice, and God stayed his hand to recognize that he was truly faithful.
As a literary story, the Binding contains several common devices; in fact, it fits quite well into Joseph Campbell's Monomyth, or Hero's Quest. Abraham is given a task (Call to Adventure) from a supernatural source (God) and sets out on a quest. His goal is met with struggle (Abraham's own doubts, according to commentary) and he encounters fantastic things (the angel of God staying his hand, the miraculous appearance of a ram stuck in a bush) to claim his victory (proof of his faith). He receives great rewards (blessings of descendants and victory over enemies) and returns home with gifts (his family has many children, and in his prosperity he is able to find good wives for Isaac).
Abraham acts as the protagonist, with a difficult -- even impossible -- task, that of sacrificing his only son. However, his faith is strong enough that he acts only in his God's will, and although the story is so short that it encompasses only the brief overview of the monomyth, it still shows setup (God's command), tension (will Isaac die for Abraham's faith?), and resolution (Isaac lives as a symbol of faith).