Marbury v. Madison was heard by the Supreme Court in 1803. At this time, the Constitution was still young, enacted only 14 years earlier. The full powers of the Supreme Court were still being worked out in practice.
This case involved a dispute that called the range of the Court's authority into question. After hearing Marbury's case, in which he correctly claimed he was illegally denied his rightful position as a justice of the peace, the court found it did not have the power to force James Madison to deliver his commission—which would make Marbury a judge—even though Marbury was legally in the right.
In making its determination, the Court had to look at the Judiciary Act of 1789, which Marbury claimed gave the Court the power to compel Madison. The Court found the Judiciary Act violated the Constitution because it assigned the Court powers not stipulated in the Constitution.
This established the concept of judicial review—the power of the Supreme Court to declare laws unconstitutional if they conflict with the Constitution. Judicial review has been an accepted function of the Supreme Court ever since.