Why do dogs like to bury their belongings?

It's because the wolf is in the body.

Chewing on bones is one of the dog's favorite recreational activities. If a bone is so loved by him, he will even bury it.
To humans, such behavior seems strange, so why do dogs spend so much energy to bury their valuable possessions?
"The reason dogs bury things is to save them for later" ,Teyotie Anderson, a professional dog trainer and behavior consultant in Florida, told Live Science. "If you don't know when you'll find your next meal, then hide the leftovers."
The act of burying bones is a form of "food caching", where existing food is stored for later use. This behavior is common in many bird and mammal species, including the gray wolf, the ancestor of the domestic dog, and is an instinct inherited from dogs.
A 1976 study in the journal Ethology showed that although wolves, known for their shrewd hunting skills, tend to stay in scavenging areas long enough to completely devour their prey, they occasionally carry and bury their prey. (Wolves and other canids are known as "dispersed hoarders," meaning they hide leftover food in a fairly large area.) This study shows that even wolf pups will hide food and move their hiding places to avoid detection by their siblings. So, when dogs do these seemingly unusual things in your home, rest assured - they are just following their instinctive "wolf nature".
Now, most dogs don't need to store food because their doting parents feed them, but that doesn't mean their natural urge to hide things for later doesn't exist. Sometimes the instinct to hide has nothing to do with storing food or protecting it from scavengers. According to canine behaviorist CesarMillan, burying may be a way for dogs to savor treasured items so they can enjoy them again. It could also be a way for a bored dog to initiate play with its owner, or a way for an anxious dog to reduce stress.
Meanwhile, some breeds, such as terriers, are only more likely to dig, whether it's to bury food or to dig for no reason at all. Andersen said, "Dogs raised exclusively for hunting or chasing small animals tend to enjoy burying toys, bones and food." Thus, it is not uncommon for dachshunds to bury bones under the pillows of the sofa". Anderson adds that if a dog does not have the instinct to hide, it should not draw attention to itself.

Dogs that have a "burying" instinct seem to go through their hoard whenever the mood strikes them." Some dogs hide their food and leave it alone for a week. Some dogs seemed indecisive, moving their loot 20 times before they settled on a spot. Some dogs bury their bones and forget about them altogether.
If a dog fails to retrieve it, you can bet that it's not because it forgot its location. Dogs have a very acute sense of smell, 10,000 to 100,000 times more than humans, according to a study in the journal Applied Animal Behavioral Sciences, so remembering where they are hiding is not a problem.