A black forum is a locked forum with a hidden registry. Only members in a user group that has access can post or view content in said forum. For all others the forum is essentially invisible. They will not see a listing for said forum, and were they to try and link through they would be stone walled or redirected be it back to a main page or to an unrelated site entirely.
The Black is probably a reference to Black Projects run by the military. Which are classified, and are not acknowledged to exist. For example Area 51 is a Black facility. The Stealth Bomber was a Black project.
I am actually somewhat amazed that so few of you are actually aware that such forums exist. Almost every site with forums has a black forum for use of staff. You do not see it, but you suspect that it is there. Ask the moderation staff here about their forum.