That "secret" classification isn't mysterious. You do any work for military contractors or intelligence agencies and you will realize that they slap a "secret" classification on lots of mundane materials -- maintenance manuals, internal phone directories, etc. It generally goes "confidential" "secret" "top secret" (and there are various classifications above top secret but anyway). The working definition is that "secret" materials are materials that, if released, would cause harm. Obviously, you wouldn't want to be circulating, say, a maintenance manual for a jet fighter, to someone without a need to know.

The real reason that ask for that is requiring a "secret" clearance will generate a security background check on someone they hire. Nothing that mysterious -- it's mostly just bureaucracy. (and never think that working for an intelligence agency is exciting -- imagine working for CNN if it was a poorly funded government agency with lots of bureaucratic rules and internal political turf fights)