(A) he name of one of the courts of the United States. It is held by a judge, called the district judge. Several courts under the same name have been established by state authority. Vide Courts of the United States. (B) In federal court and, in some states, the name of the main trial court. Thus, if you file suit in federal court, your case will normally be heard in federal district court. States may also group their appellate courts into districts -for example, The First District Court of Appeal.