The introduction to the article says:
These results indicate that the domestic dog originated in southern China less than 16,300 years ago, from several hundred wolves. The place and time coincide approximately with the origin of rice agriculture, suggesting that the dogs may have originated among sedentary hunter-gatherers or early farmers, and the numerous founders indicate that wolf taming was an important culture trait.In the German magazine Partner Hund I read that the study suggests that dogs were first used as food. At first glance that seems disturbing, but I guess it's very likely to be true.
I'm not clear about the methods of the study, as I'm no scientist. The only thing I know about mitochondrial DNA is that it can be used to trace ancestry through a female line - I think it's used because this part of DNA is handed down from mother to child unchanged. I once read a fascinating book about the origins of modern humans (written for public consumption, not for scientists). It was called The Seven Daughters of Eve.
For an interesting explanation of this type of science, Nova Online has a good article.