The story is that as Benjamin Franklin emerged from Independence Hall at the close of the Constitutional Convention in Philadelphia on September 18th, 1787, a woman asked him, "Well Doctor, what have we got, a republic or a monarchy."
Mr. Franklin was said to have replied, "A republic, madam, if you can keep it."
Perhaps the woman was being cynical, as the convention was never considering a monarchy, but of the two options that were discussed in those argument filled days, we had the option of a republic or a confederacy. There were a dozen different forms that a republic could have taken, and at least as many that a confederacy could have taken.
The founders knew about these other kinds of governments. They had just seen their children killed in battles to free us from a monarchy, and many of those in the constitutional convention had been part of a varied and interesting range of governmental experiments. Nearly every colony had tried something different - from no government at all, to direct democracy where everyone voted on everything. Oligarchy had been tried where the wealthiest ruled over everyone else, and mini monarchies were not uncommon. They tried it all, and out of their direct and personal experience, they decided that no man is capable of ruling a country.
Thus the form of government that we enjoy today. We are a Constitutionally Bound Representative Republic. Our monarchy is a piece of paper, democracy is forbidden as a form of government, and we do not vote on our futures, we vote on people to do that for us. We have the most stable and rigid government of any peoples, ever.
Our leader, the piece of paper, is well crafted. IT lays out how our government will work, who will do what, and how it must happen. It does not get tired, does not get moody, and will never scream, "Off with his head!" as so many rulers in the past have done. It does not care about you, or me, or anyone else, because it is just a piece of paper. It's mind is made up, and it's decisions have already been made. There is no arguing with it, nothing you will ever say will change it's mind, it is just a piece of paper. It takes a majority of our nation to change it, and it takes a majority to change it back. It was designed that way. It is the best Master we have ever had as a people, and it's still just a piece of paper. It is our King.
Why a piece of paper?
Because it doesn't change. If they lay out a solid government and people abide by the rules laid out in the document, then the government will never be fickle, will never change, and will stay reliable and solid for the lives of many generations. While our Great Experiment has been going on, nearly every nation out there has had a government change. But we enjoy the same protections and the same piece of mind that our fathers fathers knew.
So what did we really get?
We got upper level democracy and lower level rule of law. We got three branches of government set at each others throats, on purpose.
Congress is a democracy with protections. Instead of just a senate, we were given a congress made up of two houses. One appointed by the governors of each state, our senate, and one elected by the people, the House of Representatives.
They were given different roles. The Senate makes laws because they were felt to be more impartial. The House approves laws because they were felt to be closer to the people and would stop the bad laws. The House was given the task of spending money for the government, and the Senate was tasked with making sure that the money they spent was spent properly.
The President was to be the face of our nation. He's not a ruler, or a leader. He's the people's choice as a representative to other nations, he's in charge of the laws and given the task of making sure that they are enforced properly and impartially. He was given the job of negotiating treaties, dealing with invasions, and generally being the top law enforcement agent in our nation.
The Supreme Court was tasked with appellate powers. This means that the Supreme Court can review any lower court case that an appeal is requested - or on their own merit. Cases of ambassadors trials, public ministers and in cases where the state itself is party, the Supreme Court has first jurisdiction. What their job is, is to make sure that justice is fair, impartial, and evenly handed out. They also rule on the constitutionality of laws and make sure that the conform to the Piece of Paper.
All three of these offices are made to work together, but are also made to cancel each other out. For instance, if they dislike a Supreme Court decision Congress can amend the Constitution. The president can veto a bill, but Congress can override his veto. The system is called Checks and Balances and when it works correctly, and little gets done when the government tries to do things they are not supposed to be doing.