A court's power to hear and decide a case before any appellate review. A trial court must necessarily have original jurisdiction over the types of cases it hears.
Nearly all of the cases considered by the U.S. Supreme Court come to it from other courts (Federal or state) on appeal -- or more accurately via petitions for a "writ of certiorari." However, under the U.S. Constitution (Article III, Section 2), the Supreme Court has "original jurisdiction" over several small but important categories of cases. That means, quite literally, that the parties can bring such disputes directly to the Supreme Court. The categories are defined in terms of who the parties are.
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.
Rule 17 of the Supreme Court Rules governs actions based on the Court's original 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.
Typically, the disputes between states coming to the Court involve conflicting property claims. Two recent examples include Louisiana v. Mississippi (decided in October 1995) and Nebraska v. Wyoming (decided in May 1995).