1) in the federal court system, the entry-level trial court where most cases—civil and criminal—begin. Each federal district court sits in a "district," consisting of all or part of a state. For example, the state of Kansas is one federal judicial district. All federal trial courts sitting in Kansas are designated as a "United States District Court for the District of Kansas."
2) An entry-level trial court in some states. States may also group their appellate courts into districts—for example, the First District Court of Appeals.