It was a new idea for its time; what led the authors of the Constitution to create it instead of a monarch or pure parliament/congress? Why put so much power in one person's hands if you want a republic, and why limit them so much if you want an autocracy?
During the Revolution England's Parliament wasn't as powerful as it is now, they still had a strong executive, the king. The United States experimented with a government that had a virtually non existent executive under The Articles of Condederation. This system was deemed weak and incompetent.
So when the Founding Fathers drafted the new constitution it was generally agreed that they needed a strong executive branch to unify the states and enforce legislation. The most common form of executives at the time was a monarch, but the States didn't just fight a war to replace one king for another. So they drafted a system where an executive would be elected by the people to lead the state for a limited term at which point he could be elected again or be replaced by a new executive.
This solves the problem where in monarchies the only way to replace a reigning monarch is to either assassinate, rebel, or scare the monarch into abdication.
Source: Basic US History and Government classes. Feel free to delete this if someone with real credentials posts.