Original jurisdiction is a little like original sin. Everybody's heard of it but nobody quite understands it. The U.S. Supreme Court famously reviews case decisions of the highest courts of the states and also the federal Circuit Courts, resolving differences and setting precedent that lower courts must follow. But it also has "original jurisdiction" in a very narrow range of cases. In these types of cases, the Supreme Court can be the first court to weigh in, instead of the last.
TL;DR (Too Long; Didn't Read)
The Supreme Court has original jurisdiction to hear controversies between two or more states, proceedings that include ambassadors or other public ministers or consuls of foreign states, controversies between the federal government and a state, and proceedings by a state against the citizens of another state.
Jurisdiction means the legal authority to do something. When it comes to courts, jurisdiction means the legal authority to hear a particular case. Probate courts, for example, have jurisdiction over probate cases but not over divorces, while the jurisdiction of small claims courts is limited to monetary disputes with no more than a set amount at stake.
Original jurisdiction means having the legal authority to hear something first. The system of appeals in the courts gives several courts jurisdiction to hear a particular type of case. One court must hear it first, however, and that court is said to have original jurisdiction, the power to hear and decide a case before any appeals.
Original Jurisdiction in State vs. State
The Supreme Court is the highest court in the land, the final stop in the appeals process. Most of the cases it hears are appeals from state Supreme Courts, or, in federal court, appeals from the Circuit Courts. But the U.S. Constitution also gives the Supreme Court original jurisdiction in a narrow range of cases. That means that, in those type of cases, the parties may bring the case directly to the U.S. Supreme Court. Note that the Court is not obligated to hear these cases, but it can, at its discretion.
First, the Supreme Court has original jurisdiction to hear controversies between two or more states. In this, it has not only original jurisdiction, but exclusive jurisdiction. The parties can bring the case directly to the Supreme Court, and they cannot bring it anywhere else. No other court has jurisdiction to hear these cases.
The most important kinds of suits between states have been boundary disputes. In fact, between 1790 and 1900, the only suits between states that the Supreme Court heard were about disputed boundaries. By the twentieth century, the Court began to hear other types of original state vs. state disputes, like water-rights cases and cases related to the use of state economic, regulatory or tax powers. Typical of this kind of suit is Maryland v. Louisiana (1981), that involved a challenge to Louisiana's severance tax on natural gas.
Over the history of the Court, it has heard less than 200 state-versus-state original cases. That comes down to less than one per year.
Other Areas of Original Jurisdiction
The Supreme Court also has original jurisdiction to hear cases in which ambassadors or other public ministers or consuls of foreign states, are parties. These do not arise every day. Only two of the original cases heard by the court have been heard under the "Ambassadors" section of the clause. Still, only the Supreme Court can act with the authority to resolve these types of diplomatic encounters between contending sovereigns.
The Court also has original jurisdiction to hear controversies between the federal government and a state, and proceedings by a state against the citizens of another state.