It's an important issue in several ways. The question originally was whether L. familiaris is a different species than L. canis, or whether they are subspecies within a single species. Recent genetic data indicate that dogs did not evolve from the sort of wolves we have today, but that both wolves and dogs evolved from a common ancestor which is now extinct.
The genetic data now suggest that dogs separated from wolves about 27,000 years ago, which probably means that they were associating with humans that far back. While it's not certain, that would explain why we see more genes for amylases (dogs have a higher tolerance for human diets than do other canids) and why they and wolves have more differences in nuclear DNA than in mitochondrial DNA.
One really interesting finding is that humans adapted to association with dogs as much as dogs adapted to humans. The symbiosis seems to have been voluntary on both sides, a symbiosis that left dogs more hominid-like, and humans more canid-like. It's why we tend to have dogs even when they are no longer working with us for a living. We are made to have those four feet trotting behind.
So the research tells us a little more about us.