The Framers of the Constitution wanted to create a government that was powerful enough to take care of business, but not so powerful that it could threaten tyranny. One key idea in designing such a powerful, but limited, government was the doctrine of separation of powers.
In old-fashioned monarchies, the key powers of government—the power to make the law, the power to enforce the law, and the power to judge the law—were all held by one person: the king. The king, claiming to rule by the direct authority of God, could do pretty much whatever he wanted. (Check out the story of King Henry VIII for one of your more gruesome reminders of why that probably wasn't the best idea!) In Britain, the center of power eventually moved from the royal family to the Parliament. But still, there was no division of powers; Parliament held not only the legislative power (like the US Congress) but also the executive and judicial powers. During the American Revolution, most folks on this side of the pond came to the conclusion that this concentration of power in Parliament had turned the British Empire into a tyrannical system of government. (James Madison, in fact, famously declared "the accumulation of powers" under such a system to be "the very definition of tyranny.")
Thus when they designed the Constitution of the United States, the Framers insisted upon the separation of powers. Only the legislative branch (Congress) has the power to make law; only the executive branch, (the President) has the power to enforce and administer the law; only the judicial branch (the Supreme Court) has the power to judge and interpret the law.