The Judicial branch, consisting of the Supreme Court and a system of lower courts, is one of three branches of the American government laid out by the Constitution to provide a system of Checks and Balances. Its function is described Article III of the US Constitution. Its purpose is to interpret the law (the executive branch carries out the law and the legislative branch makes the laws).
The words written on the entrance of the Supreme Court building summarize the purpose of the judicial branch: "Equal justice under law."
The Chief Justice is the administrator in charge of the federal court system.
All federal judges are appointed by the president and serve for life. There are nine justices in the Supreme Court.
The Judicial branch was thought by the Founders to be the least dangerous branch of our government, because it had the power to interpret the law, not enforce or make it. For this reason, the Constitution is not very specific about the judicial branch.
The idea of judicial review (the power of the Supreme Court to declare a law unconstitutional), implied by the Constitution, but established by the ruling of Chief Justice John Marshall in the famous case Marbury v. Madison, established the Supreme Court's power. In this case, Justice Marshall declared that the Supreme Court could overrule any law passed by Congress that violated Constitutional.
While this decision provided that the Supreme Court keeps the other two branches in check, there are next to no checks on the Supreme Court, except for appointments and impeachment. Impeachment has not been used since President Thomas Jefferson failed in 1805 to secure the conviction of Samuel Chase, a member of the opposition party, although he did manage to get articles of impeachment passed. Jefferson did succeed in abolishing lower courts and thus remove judged appointed by his opponents.
President Franklin D. Roosevelt tried to seize control of the Court in 1937 by expanding it with five new members. He had huge majorities in both houses of Congress--and only needed a simple majority to pass the new law--but conservative Democrats revolted and defeated his power grab.
A History of the US; Book 4; The New Nation by Joy Hakim
U.S. Government and Politics by Paul Soifer