Has to do with weight and balance ( CG ) while airborne and landing. Center tanks, when installed on the 737, have different pump pressures ( cracking pressure ) with the largest center tank having the highest pumping pressure and the wing tanks having the lowest pumping pressure; therefore, the largest center tanks empty first followed by the next center tank, followed by the wing tanks. The CG of the aircraft will remain within limits if all pumps are turned on initially and turned off as the respective tank is emptied.
Mike