What is Federal Courts?

Legal Definition
The Federal Court system is comprised of the Supreme Court created by Article III of the U.S. Constitution and lesser courts created by Congress under Article I Section 8 power (for example, see 28 U.S.C. § 43). District courts function as trial courts. The federal system also has trial courts of special and exclusive jurisdiction that decide specific types of controversies such as copyright or bankruptcy issues. Appeals from the district and special courts are taken to the court of appeals for the judicial circuit in which the district court sits--the United States is divided into eleven circuits (plus DC and the special Federal Circuit). Appeals from the circuit courts are taken to the Supreme Court (State court appeals can also be taken to the Supreme court if the case involves a federal question such as a Constitutional issue).

Federal Courts have limited subject matter jurisdiction. They can only hear cases that fall both within the scope defined by the constitution in Article III Section 2 and Congressional statutes (See 28 U.S.C. §1251, §1253, §1331, §1332).
Legal Definition
These are the courts of the US government.
Legal Definition
The courts of the United States. See Courts of the Untted States.
-- Black's Law Dictionary