die Kreisstadt
county seat
The town or city where the administration of a Landkreis (district/county) is based.
Das zuständige Landratsamt befindet sich in der Kreisstadt.
The responsible district office is located in the county seat.

county seat
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county seat
The town or city where the administration of a Landkreis (district/county) is based.
Das zuständige Landratsamt befindet sich in der Kreisstadt.
The responsible district office is located in the county seat.

The word is a compound of 'der Kreis' (the district/county) and 'die Stadt' (the town/city). 'Der Kreis' (or 'Landkreis') is an administrative unit in Germany, comparable to a county. The Kreisstadt is therefore the town or city where the administration of this district is based.
Bad Segeberg ist die Kreisstadt des Kreises Segeberg.
Bad Segeberg is the county seat of the Segeberg district.
This word is specific to the German administrative system. A town or city is designated as a Kreisstadt because important district offices are located there, such as the Landratsamt (district office).
Um meinen neuen Pass zu beantragen, musste ich in die Kreisstadt fahren.
To apply for my new passport, I had to drive to the county seat.
The preposition 'in' is often used to indicate the location of the administration. For example, you say that the responsible office is located 'in der Kreisstadt' (in the county seat).
Die zentrale Zulassungsstelle für Autos ist in der Kreisstadt.
The central vehicle registration office is in the county seat.
capital
'die Hauptstadt' and 'die Kreisstadt' can be confused because both refer to an important administrative city. A capital belongs to a country, federal state, or region and is usually the seat of government. A county seat is the town or city where the administration of a Landkreis (district/county) is based. So the scale is different: 'Hauptstadt' fits a larger political area such as a country or federal state. 'Kreisstadt' fits a Landkreis (district/county).

Heute fährt Herr Lange in die Kreisstadt, weil er einen Termin beim Landratsamt hat.
Today Mr. Lange is going to the county seat because he has an appointment at the district office.
Berlin ist die Hauptstadt von Deutschland.
Berlin is the capital of Germany.