First he might have a bone he wants to bury. His ancestors may have dug a hole and buried part of the kill to keep it safe from poachers. Over time this could have turned out to be instinctive. Your dog burying a bone inside the backyard could be a result of that instinct.

Second a dog will probably dig a hole to get out of the heat during the summer time. When you see them laying in the hole they dug within your back yard, their mouth hanging open, tongue hanging out, it looks like they are pretty pleased with themselves.

Probably that is it but most likely they're just sweating. Dogs do not have sweat glands like us. They cool off by breathing open mouthed.