Final answer:
The U.S. Supreme Court is the highest federal court with the role of supervising lower courts, ensuring the correct application of laws, and hearing appeals from the Appellate Court. It has both original and appellate jurisdiction, with the majority of cases being appellate, where it reviews lower court decisions.
Step-by-step explanation:
The Supreme Court of the United States is the highest court in the federal judiciary. It has the authority to supervise lower courts and ensures they are applying laws correctly. Moreover, the Supreme Court has the ability to hear appeals from the Appellate Court, known as appellate jurisdiction. This means that the court can review decisions made by lower courts to determine if the proper laws were applied and the correct legal principles were followed.
While the Supreme Court does have original jurisdiction over certain cases—specifically those involving ambassadors, public ministers, consuls, and where a state is a party—the vast majority of its cases are appellate. It is in this capacity that the Court upholds its responsibility to interpret federal law and the U.S. Constitution, ensuring that citizens and states alike are treated fairly under the law and maintaining the principle of 'domestic tranquility'.
As part of the federal court system, the Supreme Court is the final arbiter in the legal hierarchy, sitting above both the U.S. Court of Appeals and the U.S. District Courts. Its rulings are binding on all lower courts. When it comes to federal law and constitutional matters, the Supreme Court's decisions are the ultimate legal authority in the nation.