In American politics, the US Supreme Court's most significant power, and the most important check that it has over the other two branches, is the power of judicial review. This has been in effect since the ruling in Marbury v. Madison (in 1803) and grants the Supreme Court the power...
to judge the constitutionality of actions taken by the other two branches. Additionally, it should be noted that the power of judicial review is not limited strictly to the federal government but also applies to the state governments as well.
This power has played a critical role in shaping the evolution of the United States ever since the precedent was first established. Within recent memory, you can point towards the dismantling of segregation, the pro-choice movement's victory regarding abortion rights in Roe v. Wade, and the legalization of gay marriage, all of which were decided through the Supreme Court's application of judicial review.
Ideally, the notion of checks and balances was intended to prevent any one branch of government from becoming too powerful vis-à-vis the other two branches, to the point of its becoming a potential threat to the people's liberty and collective well being. The power of judicial review represents a powerful example of what this principle looks like when put into practice.