The habit of burying food in modern dogs is an instinct that came from the grey wolf (Canis lupus) long ago, and originates from a phenomenon called surplus killing, where a carnivore would kill more than it could eat, and often use it at a later time.
Many, if not all, carnivores possess behaviour patterns which allow utilization of a kill at a later time, or allow other members of the same social unit or offspring to use the food.
When the prey is small enough to transport, and there are pups, it is often returned to the den.
Pups will usually remain in their den for the first three or four weeks of their lives before mother allows them to venture forth into the light. During this time the mother is quite dependant on her mate and other pack members to bring her food in the form of meat that is often regurgitated for her.
It is then fed on by the litter, and the excess buried for later use.
This is called 'caching', and is still seen today in the domestic dog (Canis familiaris).