Faster to post pics directly to the Nation with the "attach" feature (paper clip icon above the editor window). Anyway, that's the vacuum distribution box, aka vacuum manifold. Oh, actually, if it's a single-fitting thing all by itself, with an electrical connector, and at the OTHER end of the hose is the distribution/junction box, then the thing that's broken is the low vacuum sensor. It's the thing that turns the BRAKE light on. One option, to tide you over, is to disconnect that hose from the distro box, at the other end, and put a vacuum cap/plug on that fitting. That would at least restore vacuum to the brake booster and HVAC controls.
Hmm, let's go see if RockAuto might have that part....
Edit - nice; RockAuto has the electrical connector for the sensor (aka low vacuum switch). Also available on eBay. Not the switch itself, though. You're probably looking at a junkyard or part-out.