The role of the Supreme Court among the three branches of government is to act as a check on the other two branches. The Supreme Court is to make sure that the Constitution of the United States is adhered to.
The Constitution sets out a number of things that the government is not allowed to do. This is a major component of our freedom as American citizens. Because we know that there are things the government cannot do (unreasonable searches and seizures, for example) we know that our freedoms are secure. But who prevents the Congress and the President from doing things that are contrary to the Constitution? This is where the Supreme Court comes in. It has the right to decide when actions of the elected branches are contrary to the Constitution. When it does so, those actions may no longer be taken. By ordering the other branches to cease to violate the Constitution, the Supreme Court protects our rights and our constitutional system. This is the main role of the Supreme Court as one of the three branches of government.