It may seem obvious to us humans to hide our excreta, but this is not quite normal behavior for animals.
Interestingly, dogs have the habit to pee all over the place. It's know that they do so to mark their territory. So when they want to mark their territory, why do they cover up their poop?
I found an old web article where someone asks the same question, without getting a credible answer. He quotes a Yahoo Answers answer making the following claim:
This behavior is natural in dogs. They cover up their "waste" so that an enemy does not find them, from the scent of the poop or pee. It is an instinct handed down from wolves, who hid their scent by covering up their feces in leaves, sticks, soil, or other nearby natural materials. They also rolled in animal carcasses to hide the scent of them. Your dog is just using her natural instinct to protect herself from predators.
Another things that dogs do, called marking, is when the dog pees in a certain area. They do not cover it up, as it is marking a territory as their own. Male dogs usually do this on trees, wooden posts, furniture, and other things. Female dogs do this in heat. Dogs do not poop to mark something, only pee. When you dog pees or poops and then covers it up, this does not mean she is marking her territory. Just wanted to add it so you don't get confused. :)
I find it hard to believe these two opposite claims. One time dogs want to mark their territory and the other time it's scared from predators. I know many dogs that do not cover their pee, but do cover their poop, sometimes even within the same walk (and so the same territory).
If this is true, why do dogs do both in the same walk?
On Wiki Answers I found this answer:
The animals are not actually covering up the pee or pooh but spreading their scent. This often happens with animals that are dominant (for instance show dogs).
It's so that dogs never actually cover their poop anymore, they only perform some random scratches, throwing a little sand on the turd, sometimes even nothing. That fact makes this answer quite more likely than the previous one.
Another take that's similar to the previous one is this one from Dogster:
So, why do dogs scratch with their hind legs after defecating? You might think the dog is trying to cover up his poop like a cat does, but it’s actually a way to mark territory, with the scratch marks in the ground pointing to the scent the dog has left.
I also found an eHow article on this subject. It seems to agree with the previous two explanations, but is more detailed.
It is normal for dogs of both sexes to vigorously kick the ground with their hind legs after defecating. This is called scraping or peeling out. Some dogs will also do it after urinating. Dogs are descended from wolves, which also perform this behavior. It is not a bad habit, but a vital part of a dog leaving a visual message and scent message to any other dogs that happen to pass by.
They also say that the specific reason why they spread scent with their paws is because paws just contain a lot of scent.
Dog paws contain scent glands. There are also glands in between the toes. The action of scraping the paws against the ground helps release the scent inside of the glands. Dogs scrape the ground in order to increase their scent on the area near the feces pile, according to veterinarian Dr. Justine Lee. Before domestication, dogs wandered in large territories. One vital way to communicate with other wandering dogs is through scent marking. This instinct has not been bred out of the domestic dog.
So, which theory is the most valid? I tent to go for the scent one. Any additions?