Federal jurisdiction means that the federal court has the legal right to hear a case and decide what happens to the parties involved in it. In order for a court to decide what happens to you — or to adjudicate your dispute — that court has to have the right to compel you to do something. Courts get that right through personal jurisdiction. The court also must have an interest in deciding a case dealing with that particular subject; family court, for example, would not have much interest in deciding a car accident lawsuit. This is referred to as subject matter jurisdiction.
In the United States, there are two main court systems that could have jurisdiction over a case: the federal court system or the state court system. Federal courts include the US Supreme Court, the Courts of Appeals, and bankruptcy and tax courts. State courts include individual courts within each state, as well as family courts and small claims courts. According to the US Constitution in Article III, the federal courts are courts of limited jurisdiction, while the state courts are courts of general jurisdiction. That means that the state courts have a wide subject matter jurisdiction and are interested in and get to hear a lot of different cases, while federal jurisdiction is limited to cases in which the Constitution has expressly stated that the federal court has an interest.
Therefore, for federal jurisdiction to exist, specific conditions must be met. There are two ways in which a federal court can obtain federal jurisdiction over a matter. The first way is if the case arises out of a federal question or law. The second way is called diversity jurisdiction and exists if the two parties involved in the lawsuit are from different states or have different residencies and if the dispute is about more than $10,000 US Dollars (USD).
Federal question cases are cases in which the two parties are having a dispute that federal law will decide. For example, if one party believes that a law is unconstitutional, the case will have to be decided in federal court because the question will require the interpretation of the Constitution and because the dispute "arises" out of or is based on the Constitution. Likewise, if a person sues under federal laws, such as the Civil Rights Act of 1964, federal jurisdiction exists because the case arises out of a law passed by the federal government.