federal judiciary of the United States is one of the three co-equal branches of the federal government of the United States 
What are they responsible for?
The President with the consent of the Senate to serve until they resign, are impeached and convicted, retire, or die.
But what are they in charge of?
appeals from such tribunals (unless, for example, appeals are to the Court of Appeals for the Federal Circuit.)
The United States courts of appeals are the intermediate federal appellate courts. They operate under a system of mandatory review which means they "must" hear all appeals of right from the lower courts. In some cases, Congress has diverted appellate jurisdiction to specialized courts, such as the Foreign Intelligence Surveillance Court of Review.
The Supreme Court of the United States is the court of last resort. It
Federal judiciary of the United States
The federal judiciary of the United States is one of the three branches of the federal government of the United States organized under the United States Constitution and laws of the federal government. Article III of the Constitution requires the establishment of a Supreme Court and permits the Congress to create other federal courts, and place limitations on their jurisdiction. Article III federal judges are appointed by the president with the consent of the Senate to serve until they resign, are impeached and convicted, retire, or die