The highest court in a given judicial system in the United States of America. Each state has it's own supreme court, as does the federal government (seated by 8 associate justices and one chief justice). They can choose which cases they wish to accept, can over-turn or alter the ruling of any inferior court, and can, in some cases, create constitutional law. Their main purpose is to defend the Constitution (of either their state or the federal government) and to interpret it's meaning in their rulings.
The United States Supreme Court is often referred to as 'the high court.'