A German district is an administrative subdivision known as Landkreis ("rural district"), except in the states of North Rhine-Westphalia and Schleswig-Holstein where it is known simply as Kreis. Most major cities in Germany are not part of a rural district, but perform district-like functions on their own. In this context, those cities are referred to as Kreisfreie Stadt (literally "district-free town") or Stadtkreis ("urban district").
Rural districts are at an intermediate level of administration between the German states (Länder) and the municipal governments (Gemeinden). They correspond to level 3 administrative units of the Nomenclature of Territorial Units for Statistics (NUTS 3), and are roughly equivalent to counties in the United States.
Previously, the similar title Reichskreis (Imperial Circle) was given to groups of states in the Holy Roman Empire. The related term Landeskommissariat was used for similar administrative divisions in some German territories until the 19th century.
More information on the Wikipedia page [1].