GESTAPO, and Gestapos is bad usage- you would say Gestapo agents, or men. It was the plainclothes or detective arm of the German SS and derives from the acronym- Geheime Staats Polizei=- Secret- lit,...
The Gestapo was the political secret police. Its functions included spying on enemies of the Nazi regime (imaginary as well as real), finding dissidents and opponents. They were arrested, ill treated...
They hunted the Jews, hippies, homosexuals, blacks and gypsies for the Nazi's. They usually killed them if they found them. This was in WWII for Hitler.
According to the Wikipedia article on the Gestapo it was set up by Goering on 26 April 1933 from a merger of two existing organizations. In 1934 Goering had to hand over control to Himmler and it was...