Simply put, it refers to the independence of the three branches of the U.S. government, specifically with regard to the constitutional charter given to each branch. One does not trump another, but there are checks and balances as a means of preventing one branch from exerting undue influence over another, while providing for oversight and legal authority to make inquiries, etc.
The Articles of Confederation failed because they did not give the central government enough power. It had no power to tax, to raise troops for an army, to control interstate commerce, and to stop states from printing money, among many others. So the framers of the Constitution knew that they had to create a strong federal government, but at the same time make sure it did not become too powerful. So they incorporated the principles of Separation of Powers, Checks and Balances, and Federalism into the Constitution.
The framers of the Constitution (those who framed, or wrote, the Constitution) feared a powerful central, or national, government. In order to keep the national government from becoming too strong, they divided the government into three branches, the legislative, the executive and the judicial. The framers then gave each branch separate, specific powers. This is known as separation of powers—that is, the powers of the national government were divided among the three branches of government.
The framers were also concerned about one branch of government gaining too much power; therefore, they also established a system of checks and balances. Each branch of government was given the ability to check the power of the other two branches of government.
Finally, the framers of the Constitution were concerned that a national government would dominate the state governments—that is, the national government would have too much power and the state governments would have too little power. To keep this from happening, the framers established a government based on federalism. In this system, power would be divided between the federal government (that is, the national government) and the state governments. Some powers would be given or delegated only to the federal government, some powers would be reserved to the states, and some powers would be shared—both the federal government and state governments would have that power.