Two of the most important powers the federal courts have are both the power of judicial review, and the power of the Supreme Court to overrule itself. These two powers allow the Judicial Branch to keep both itself and the Executive Branch in check, in theory providing a greater level of transparency and democracy.
Arguably the most important power the Judicial Branch has, the judicial review provides the federal courts with the power to interpret the U.S. Constitution. This effectively translates into the ability to rule certain government sanctioned laws unconstitutional, therefore nullifying them.
As a result, this allows the courts to act in the interests of the wider public, by protecting them against laws that could potentially inhibit freedom and civil rights. More than 100 federal laws have been ruled as unconstitutional.
The U.S. Supreme Court can overrule previous decisions, meaning that not only is the legal system able to adapt, but that previous rulings that do not apply to modern society as a result of ethical changes or greater understanding of the issues raised by such a case are able to be amended as necessary. One such example case is that of Brown vs. Board of Education of Topeka.