What is it?
It was a joke for the DS9 episode Trials And Tribble-ations
. And nothing more.
It wasn't presented in the episode as a joke in the Universe itself. Rather, it was presented as a real agency that actually exists in the Trek Universe.
As for what it does, not much is known about that since the novels are not canon and hence none of any of their content is applicable, and it received minimal screen-time.
I got the impression from the tone of the DS9 episode that they do indeed have arrest powers; otherwise it wouldn't make nearly so much sense for the whole crew to be fretting about their appearance.