A state supreme court is the highest court within a U.S. state judicial system. It primarily hears appeals from lower courts, ensuring that laws are interpreted and applied correctly. Each state has its own supreme court, which can vary in structure and the number of justices. The decisions made by a state supreme court are final and can only be reviewed by the U.S. Supreme Court if federal issues are involved. These courts play a crucial role in shaping state law and protecting the rights of citizens within their jurisdiction.