Maintaining dental health, and specifically preventing gum disease (periodontal disease), is considered critical to preventing a range of other health conditions, from diabetes to heart conditions.
The theory is that chronic, untreated infection and inflammation in the gums can lead to infection and inflammation in other parts of the body, especially the heart.
A large 2009 study of nearly 60,000 dogs found that, "periodontal disease was associated with cardiovascular-related conditions, such as endocarditis and cardiomyopathy. Chronic inflammation is probably an important mechanism connecting bacterial flora in the oral cavity of dogs with systemic disease."
According to the American Veterinary Dental College, "Studies in humans have linked periodontal disease to a variety of health problems including poor control of diabetes mellitus and increased severity of diabetic complications."