That hose is there to bring warm air up from by the header while the engine is warming up. If you look inside the air box intake there is a butterfly valve in there that closes when its cold to bring air in through that hole, and it opens when the engine is warm to draw in colder air from behind the front grill. Without a hose leading to the air box, the butterfly valve won't open and air will not be drawn in from behind the grill, this creates an intake restriction that can in theory hinder engine performance.