Two of the main metatarsal pad functions—restoring proper forefoot fat pad positioning and spreading out the transverse foot arch—are quite independent. In the case of the former, it's really the toe spring built into conventional footwear—and the associated toe flexor/extensor muscle imbalance it creates—that's responsible for shifting the fat pad to a position further out on the foot, closer to the ends of the toes.
Metatarsal pads, which should be positioned just behind the ball of the foot, push up in this location, which has the advantageous effect of bringing the toes back down toward the ground, where they should be. Metatarsal pads, therefore, help lengthen/stretch the too-tight, too-short toe extensors and shorten/strengthen the too-weak, too-long toe flexors, restoring balanced tendon pull on the toes. This, in turn, encourages the forefoot fat pad to shift back to its intended protective position, which is underneath the heads of the metatarsal bones.
Aside: Metatarsal pads, due to their relative softness and positioning, do not, in any way, function like a conventional arch orthotic, which seeks to restrict or limit foot motion. Instead, metatarsal pads seek to restore natural/healthy foot motion.
In terms of spreading out the transverse foot arch, again, it's really about the positioning of the pad behind the ball of the foot. In this location, the pad encourages the metatarsal heads to spread out, which has the desirable effect of giving the sensitive structures that travel through this area en route to the toes—such as nerves and blood vessels—more room through which to pass. Most conventional footwear, though widest at the ball of the foot, still squeezes/pinches this part of the foot, which, when combined with toe spring, can lead to problems such as neuromas.