The gap, which is usually about one inch, is there for air circulation. The open slot under the door is especially important when the air conditioning system is operating. The HVAC system in a manufactured home cannot effectively push air into a completely closed room when there is no way for the air that is being displaced to return to the system. The opening under the door provides a way for the air to escape and, without the gap under a door, the air conditioner (or furnace) would simply pressurize the room.
Newer mobile homes also have a louvered vent panel above the door, which also helps to provide natural air flow into the room when the HVAC system is off. Because of the difference in temperature between air near the floor and air near the ceiling in a room, a natural circulation of warmer air will go through the louvered vent above the door, with cool air pulled under the door at the same time.
