The Gestapo was the official secret police of Nazi Germany. Their name stands for Geheime Staatspolizei. This can be translated to secret state police. Under the overall administration of the Schutzstaffel (SS) it was administered by the Reichssicherheitshauptamt and was considered a dual organization of the Sicherheitsdienst and also a suboffice of the SD. Heinrich Himmler was its leader.
The Gestapo were allowed to arrest people that offended the government in any way. The government could use the secret police to accuse and arrest anyone they wanted without being questioned.