Das Standesamt is an office, usually located in the town hall, where births, marriages and deaths are registered. The office also issues the relevant certificates for these occasions.
The civil part of the marriage ceremony takes place at the Standesamt itself, often in a room specially decorated and set aside for this purpose.
Some towns have rooms, dedicated as a Standesamt in other buildings, such as the Kaiser-Friedrich-Bad in Bad Homburg or the Brauhaus in Oberursel.
If either the wife or husband is not a German national, or if one of the parents are not German, then the application to marry or to register the name of a child can get very complicated. The non-German half may be required to sign away their right to use their national laws, eg. in naming their child, in order to simplify the situation.
To hear a simple explanation and a short discussion in German, listen to the podcast:
(Press the “play” button to listen to the podcast)