This clause details exactly what kind of cases may be heard in federal courts: ones involving ambassadors, public ministers, and consuls; cases regarding admiralty and maritime jurisdiction; those in which the United States is a party; controversies between two or more States; those between citizens of different States; ones involving citizens of the same State claiming lands under grants of different States; cases between a State and a citizen of another State; and those cases in which one of the parties is a foreign state, citizen, or subject. These last two items have been nullified by the Eleventh Amendment.

The Supreme Court is unusual in that it has both original and appellate jurisdiction, as provided by this clause. It's original jurisdiction extends to cases concerning ambassadors, public ministers, and consuls, and those in which one of the parties is a State. The other types of cases, as mentioned above, fall under its appellate jurisdiction. Congress has the power to make exceptions or control this, as it sees fit.

The trial of parties for federal offenses, all of them except for impeachment, is guaranteed to be a jury trial and is to be held in the State where the crime was committed. If no State applies to this, Congress may choose the place of the trial. The Fifth, Sixth, and Fourteenth Amendments explain more about the court system of the United States and the various rights involved.