The federal court system handles issues relating to disputes about federal laws, for instance, if a law is constitutional. All other legal disputes are handled by state court systems.
The Judicial branch is split up into three main parts, the Supreme Court, Courts of Appeals, and District Courts. Disputes are initiated in District Courts, and if appealed, can move up to Courts of Appeals, and sometimes the Supreme Court (except in rare cases when the Supreme Court has original jurisdiction). The United States is split into 94 federal judicial districts that are organized into 12 regional circuits and one federal circuit, each of which has a court of appeals.
Decisions only set legal precedents for that circuit and are not binding to other circuits. All circuits feed into the Supreme Court which can create a legal precedent for the entire country.
U.S. Courts of Appeals
There are 13 U.S. Courts of Appeals, one for each circuit. These courts are appellate courts. Their job is to determine if a lower court did its job. For instance, if a murderer was convicted in a district court and the decision was appealed to an appellate court, the court would be trying to determine not the facts of the case, such as evidence, but whether the trial was held correctly, or if a law is constitutional. The courts consist of three judges and no jury, but the total amount of judges is different for each circuit. Once an appellate court makes a decision, it serves as a precedent for the entire circuit.
There are 94 district courts, at least one per state. These courts are organized into the same 13 circuits that the Courts of Appeals are in. These courts, also called trial courts are the kind of courts that people generally think of when they think of a trail. They consist of a judge alone, or with a jury. They are at the bottom of the system and are where most cases originate from.