The legal execution that defines the power of judicial review is established through the landmark case of Marbury v. Madison in 1803. This case affirmed the Supreme Court's authority to declare laws and actions of Congress or the executive branch unconstitutional, thereby ensuring checks and balances within the U.S. government. Judicial review plays a crucial role in protecting individual rights and upholding the Constitution, making the judiciary a vital component in interpreting the law and maintaining the rule of law in the political system.