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?
Supreme Court of the United States is the court of last resort.
Ah okay so they take cases that have been appealed.
generally an appellate court that operates under discretionary review, which means that the Court can choose which cases to hear, or not to
I bet they only take the most intersting cases.