Ever since the Supreme Court granted to itself the power of judicial review in the landmark case of Marbury v. Madison (1803), the judicial branch of the American government has had a very important role to play in acting as a check on the other branches. In its role as the arbiter of what is or is not constitutional, the Supreme Court is supposed to ensure that the other branches do not act in ways that violate the Constitution.
To that end, the Court has the power to strike down acts and laws that it deems to be unconstitutional. This gives it a very important role in the US system of government, allowing it to give life to the theory of checks and balances lying at the heart of American constitutionalism.
Over two centuries after Marbury, judicial review remains a highly contentious power. Some have argued that it is flagrantly undemocratic, as it represents the will of an unelected body of judges prevailing over the will of the majority. For instance, even if a particular piece of legislation enjoys widespread support both in Congress and among the American people at large, it can still be struck down by the Supreme Court if it is deemed to be unconstitutional.
Despite such controversy, however, it seems that the crucial role that the judiciary plays in enforcing the system of checks and balances means that the power of judicial review is here to stay for the foreseeable future.