The judicial branch is the arm of the US Federal government which interprets and applies the laws passed by the legislative and executive branches in accordance with the system of checks and balances. If a law is passed by Congress and approved by the President, it can still be called into question by the Supreme Court.
The federal judicial system in the United States is split into several layers. This includes 94 district courts, 13 courts of appeals, two courts of special jurisdiction, and the Supreme Court. The lower courts preside over the local affairs of their districts (there are state courts under the federal courts which mediate state law), or issues with specific focuses.
The federal courts are tasked with resolving disputes between states and dealing with federal crimes. However, when these courts are unable to reach a satisfactory verdict, or if a case is particularly controversial, it may be brought before the Supreme Court.
The Supreme Court, composed of the Chief Justice and eight associate judges, is the highest court in the United States, and its job is to handle the most difficult and nationally significant cases, especially when it comes to interpreting the US Constitution... deciding if a law or conduct is 'unconstitutional.'
They exist to handle cases which may not be covered by the current laws, so these justices are often responsible for setting the precedent in law. As in the case of Mapp v. Ohio in 1961, when the Court ruled that evidence which is illegally obtained is inadmissible.
Sometimes, a particularly controversial decision of the Supreme Court can be reversed, as it was with the Plessy v. Ferguson ruling of 1896, in which the Supreme Court decided that racial segregation of schools was sanctioned as these schools could be 'separate but equal.' In 1954 the issue was revived with Brown v. Board of Education, and the Court reversed the previous ruling, declaring that 'separate was not equal' and that segregated schools are unconstitutional.
Unlike many other important political servants, the nine justices of the Supreme Court are not elected, but are nominated by the President. They serve life tenure until they either resign or retire. Technically, it's possible to impeach them, but it has never happened in US history.
Their term runs from the first Monday of October to June or early July of the next year. This time is split into two-week intervals called 'sittings' and 'recesses.' During 'recesses', justices discuss cases amongst themselves and form opinions, then during 'sittings' they rule on those cases and are presented with new ones.
The power of the court has always been controversial among the ruling politicians. Several Supreme Court rulings have been ignored, such as in the case of Worcester v. Georgia in 1832, when both the President and the lawmakers of Georgia willfully did not comply with a Supreme Court decision.
The Court chose not to enforce their decision, however, to avoid political fallout with then-President Andrew Jackson. Several other Supreme Court rulings have also been overturned by amendments to the Constitution, which shows that even the highest judges in the land are subject to checks and balances.