Thin hose connected by engine?

Looks like the inlet hose for the PCV system. Basically it draws fresh air in through the airbox, that circulates around in the engine collecting fumes and then gets put into the engine at another point so it can be burnt. That way you are not dumping those fumes out into the world. It also looks like it was replaced with generic hose as the original is a molded hose that comes out and bends up at a 90 then another 90 onto the fitting. There should be a rubber grommet in that hole for it to plug into.