The Supreme Court of the United States generally has appellate jurisdiction over its cases; i.e., cases are appealed through the judicial system until they reach the Court, most commonly through writ of certiorari. However, in a limited class of cases, the Court has original jurisdiction to consider the facts and the law of a case without it having first been passed on by a lower court. Currently, the only original jurisdiction cases commonly handled by the Supreme Court are disputes between two or more U.S. states, typically regarding boundary lines, water claims, or other property issues.
The original jurisdiction of the Court is laid out by statute in 28 U.S.C. § 1251. Section 1251(a) provides that with one type of dispute (disputes between states), the Court's jurisdiction is not only "original," it is exclusive. In other words, if the parties cannot settle the matter, no other court but the Supreme Court has authority, under the Constitution, to take jurisdiction.
Relatively few original jurisdiction cases come to the Court. In recent times there have been one or two a year. The Court's practice in these cases is to appoint a "Master" to hear the evidence, determine facts, and recommend a decision. This allows the Court to deal with the dispute very much like it does with those that come to it on appeal, for it puts the Court in the posture of reviewing the Master's findings and recommendations in the light of legal arguments made by the opposing parties.
Federal courts are granted original jurisdiction in cases involving interpretations of United States laws, maritime law, cases involving citizens of different states, cases between ambassadors and representatives of foreign nations, cases between state governments, and cases in which the United States is a party.