Here's what happened:
* Voldemort attempted to steal the Stone: He believed it would grant him immortality and a physical body.
* Harry and Quirrell fought over the Stone: In the final confrontation, Quirrell was possessed by Voldemort.
* The Stone was accidentally destroyed: During the struggle, Quirrell's touch caused the Stone to disintegrate into dust.
So, while Harry wasn't aiming to destroy the Stone, his actions (or rather, the actions of Voldemort within Quirrell) led to its demise.