According to the Cornell University Law School, the powers of American federal courts come directly from the U.S. Constitution, Article III. Section 1 provides for the creation of the Supreme Court as well as "inferior" courts.
Section II specifies who and what are under the jurisdiction of federal courts. For example, according to the United States Courts website, the Supreme Court hears cases between states, cases that involve government ministers or any appealed cases that concern constitutional or federal law. The United States Courts site also describes the many varieties of lower federal courts. Some of these are the Court of Appeals, Bankruptcy Courts, District Courts, Tax Court and Court of International Trade.