The U.S. Supreme Court ruling in Marbury v. Madison (1803) is significant as it established the principle of judicial review, allowing the Court to declare laws unconstitutional. This landmark case arose when William Marbury petitioned for his commission as a justice, a decision that Chief Justice John Marshall deemed unconstitutional. By asserting that the Supreme Court had the authority to overrule both Congress and the President, this ruling laid the foundation for the judiciary's role as a co-equal branch of government, significantly influencing the balance of power in the U.S. political system.