When a dog uses his muzzle to move his food bowl around, he's responding to ancient survival instincts found in most wild predators. This could be expressed as "bury it deep in order to keep."
If a dog is full and there is still food in the bowl, he may try to save it for later. Wild canines, including wolves, coyotes and foxes, have been observed to bury a partially eaten carcass and come back later to dig it up and eat more. This is especially true if they are raising babies. Since they have no hands, their only way to transport food is in their own stomachs, which can hold only so much. They bury the excess food and return for refills as long as the food lasts or the pups are hungry.
Some dogs will move their food bowls into a secluded corner, push them under furniture or cover them with whatever they can find, including towels, rugs or your best shirt out of the laundry basket. In the wild, a tiger that can't eat his whole kill at one sitting will drag it away from the kill site and cover it with dirt, leaves and branches to hide it from scavengers until he can digest what he has eaten and polish off the leftovers.
Burying or covering food helps keep it from drying out in the sun or freezing in the snow-- in other words, it keeps it in the most edible and nutritious condition. Most predators are opportunistic scavengers and will eat meat in even an advanced state of rottenness, but prefer fresher food if they can get it. However, the nicest dog will eat the most disgusting trash if he can get at it.
A leopard drags a dead antelope into the treetops to keep it from hyenas. Crocodiles store their kills underwater until the carcass is soft enough to tear apart and swallow. People carry food home from the supermarket and put it in pantries, refrigerators and freezers until they're ready to eat it. Domesticated as they are, dogs bury bones and move their food bowls because they retain some of their wolf ancestors' survival techniques.