The metal/glass shroud acts as a deterrent to the spread of a stovetop fire, and helps to collect cooking fumes. The fan performs either of two actions:
It draws fumes and odors up or down--depending on the style of vent hood--through a grease filter inside a duct system and out of the house.
Or it draws fumes and odors over an activated-charcoal filter and recirculates the air, back into the room.