Federal courts are sometimes referred to as Article III courts, as the judicial authority of these courts was established in Article III of the Constitution. The Constitution is the supreme law of the United States, so no state or state court can establish a law that contravenes it. That is why the U.S. Supreme can hear cases that began in federal court or in state court depending on the matter being disputed.
Unlike state court judges, federal judges are not elected. They are nominated by the President and confirmed by the U.S. Senate. They serve for life, barring a congressional impeachment.