The theory behind a facepulling headgear is rather simple. You want to apply constant forces on the palate to move it forward, upward and to expand it. Creating a headgear that is light enough to be worn for hours and that is comfortable enough to sleep with is the challenge.
First, there is the forward force. The biggest surface to apply this force is the anterior region of the palate, from where it will drag the maxilla forward. A forward force alone is problematic, because it would rotate the maxilla in a counter-clockwise direction and disrupt a healthy bite.
An upward force needs to be added, that will try to elevate the maxilla in the skull and create a clockwise rotation to counteract the forward force. When F1 and F2 are applied at the same time, the maxilla will move as a whole, without rotation or disruption of a healthy bite.
Finally, a transverse force is added to expand the maxilla by pushing on the walls of the palate. This is widen the midface and promote bone growth, since the skull is being stretched out in 3 directions simultaneously. This process is called sutural distraction osteogenesis.
It is EXTREMELY IMPORTANT that the teeth do not experience any of these forces. Trying to expand the adult maxilla through teeth-anchorage is a bad idea, as the teeth will move way before any bone growth occurs.