The box, called an oil trap or oil separator, has passages in it to separate oil vapor from other combustion gases (directing some of the former back to the crankcase), and leads along a hose to the flame trap (a plastic, or earlier metal) screen, and from there to the throttle body.

That box and the flame trap must be kept clear -- they're important maintenance items -- or else (unless you use synthetic oil, which seems to keep everything clean) it will result in positive pressure (it should normally be a slight vacuum) in the crankcase that will blow out seals.