The behavior stems back from when our dogs were wolves and wild dogs, trying to survive in the wilderness. When dogs kick up grass or dirt (or even just go through the motion of kicking) after they've finished doing their business, they're not actually trying to cover it up - they're sending a warning to other animals.
"It href="http://www.proiettovets.com/"> is not that they are covering their eliminations, they are enhancing it. Dogs do this for communication purposes," Dr. Robert Proietto, a veterinarian in New York City, told The Dodo. "Much like deer and other animals who scrape the ground or rub antlers on trees to communicate with each other."
When dogs kick their feet against the ground, they emit a scent from glands in their paws that helps them to mark their territory and tell other animals that they've been there, according to Dr. Proietto.