Which organ of government is known as the judiciary?

I think you are referring to the form of government that the United States and some other countries have, with a legislative organ, an executive organ, and a judicial organ.  We usually refer to these as branches of government.  When we make reference to the judiciary, we often mean the Supreme Court of the United States, which is meant to have nine members, although there is a vacancy at the moment.   The Supreme Court was established by Article III of the Constitution.  The legislative branch, Congress, has established other courts below the Supreme Court, federal district courts and federal circuit courts.  The district courts are throughout the United States, and they are trial courts to make determinations about federal laws and the Constitution.  The circuit courts are appellate courts, and anyone has the right to appeal a district court decision to the circuit court.  From the circuit court, one may ask the Supreme Court to review the decision, but it is up to the Supreme Court to agree to do so or not.  At the state level, there is also a judiciary, established by each state's constitution.  There are three levels here as well, a trial court level, an appellate court level, and a state supreme court level.  As in the federal judiciary, one has the right to appeal the decision from the trial court to the appellate court, but the state supreme court decides whether or not to hear an appeal from the appellate court decision. 
https://www.fjc.gov/history/home.nsf