The Root of the Behavior
Another plausible explanation is the act of defecating itself is not only a welcome relief, it also feels good to our dogs. When our dogs have been pent up in the house all day without access to going outside, they will feel a sense of urgency to eliminate as soon as they have the opportunity for a good romp in the yard. As a result, our dogs do a form of a victory dance because they feel so light and free now that the poop is gone. When our dogs have a poop, they sometimes end up with some "residue" stuck to the hair surrounding their anus. Some dogs don't seem to notice this and continue about their day. But for other dogs, this sensation is irritating, and they want to do something to solve the problem. For many dogs, this includes a scooting of their bottoms across a grassy area to try to rid themselves of the offensive material.
Encouraging the Behavior
Dogs who have issues expressing their own anal glands often require veterinary assistance. The sensation of having anal glands that are overly full is most definitely unpleasant, and your dog will seek release from this uncomfortable situation. Another possible explanation for this strange euphoric running following a poop is the marking of territory. This phenomenon is usually evidenced first by a digging or burying motion after the dog has defecated. In the wild, it would have been important for a dog to bury his poop to hide his "scent" from potential predators. But there is more to it than this. Dogs contain powerful scent glands in their feet. When they paw at things or dig, they release their own unique fragrance in that spot, thus marking a place as theirs. The act of doing this lets other dogs know that they have claimed a space as their own. In the case of running after a poop, your dog may be marking your entire yard with his scent. If so, he is sending a message that is loud and clear; your yard is for his pooping enjoyment only. Dogs of the neighbourhood, take note!
Other Solutions and Considerations
Thankfully, this behavior is rather endearing and comical to watch. You might want to fetch yourself a cold drink and settle in to watch the show. It just might be the best laugh you've had all day! If you witness your dog enjoying a rather vigorous romp after a good poop, rest assured that this is perfectly normal dog behavior. In general, it is not destructive nor a cause for concern. However, should you fear for the potential of destruction to your property, you could choose to take Fido for several walks a day when nature calls. By keeping Fido on a leash, you will restrict his ability to take off on a frenetic post-poop run. If you opt to do this, always make certain you have plenty of poop bags with you to properly dispose of all waste materials. Your neighbors will thank you for it!