What is the difference between original and appellate jurisdiction, and which type of jurisdiction does the supreme court have?

Original jurisdiction refers to a court's ability to hear a case before anyone else can review it. Appellate jurisdiction refers to the review of the proceedings done before a court with original jurisdiction. In short, this means that a court with appellate jurisdiction can review what the lower court has done to see if they did it right.

The Supreme Court is (mostly) a court of appellate jurisdiction. It has original jurisdiction if an ambassador or other foreign official is involved. Most often, the Supreme Court has original jurisdiction when states are fighting over water rights.