The Supreme Court, the Judicial arm of the government, acts as an interpreter and arbitrator of the Constitution of the United States. In essence, it rules, or adjudicates, on previous rulings which have been challenged for their constitutionality. Thus, the Supreme Court is the final court of appeal from inferior federal courts or from state courts if a constitutional issue is involved.
One recent example of a case that reached the Supreme Court is that of Schuette v.Coalition to Defend Affirmative Action, which involves the ruling of the state of Michigan that bans the consideration of race regarding college admissions. Justice Anthony Kennedy wrote the opinion of the plurality of the Court:
[We] concluded that there is no authority in the Federal Constitution or in this Court’s precedents for the Judiciary to set aside Michigan laws that commit to the voters the determination whether racial preferences may be considered in governmental decisions, in particular with respect to school admissions.”
This ruling underscores the role of the Supreme Court as that of an impartial arbitrator of the Constitution. The Supreme Court determined that it did not have the right to resolve the debate over racial preferences being given in college admissions. This was for the lower courts, namely that of Michigan, to decide.
While this decision upset many, it does exemplify the Supreme Court's independence from the current political pressure that exists around it in the other branches of government; indeed, it is a judicial system governed by the Rule of Law, which is how the Founding Father's designed it. In this way, it remains independent, for the most part, of politics and strictly supports the U.S. Constitution, as it should.
Adjudicate means "to pronounce or decree by judicial sentence". The Supreme Court decides which cases to act on based on which ones Congress or the President passes down. Their job is to decide if the case is constitutional or not, meaning does the case follow the laws of the Constitution or break them.
The two ways that cases can be passed down to the Supreme Court is by direct appeal from lower courts or by petitioning for a writ (done by the four justices of the Supreme Court) if a constitutional issue is noticed.The reason the Supreme Court can only adjudicate is because it limits their power (following checks and balances) and because the Constitution states in Article 3 that
"The judicial power of the United States shall be vested in one Supreme Court and in such inferior courts that the Congress may from time to time ordain and establish."