That door, behind the nose gear, gets fully retracted when the gear goes up.
On the ground, while you are taking off, it acts as a fender, reducing the amount of debris that would get slung onto your lower fuselage, and by extension, into the rear prop.
Also, in flight, it smooths the airflow behind the gear doors. Without it, you would have a large hole.
http://www.youtube.com/watch?v=PDTDgLZ1mJE