The most common dental problem that we find in pets is called periodontal disease.
The word "periodontal" means "surrounding the tooth". This is disease that affects the attachments of the tooth into the socket. The normal tooth has one to three roots that are long and strongly held to the bone by a ligament. This is a very tight bond. Imagine having a bucket of set concrete into which a hole 8 inches deep and 3 inches wide has been drilled. Coat the inside of the hole with a strong epoxy glue several millimeters thick, then fill the hole with another batch of cement and allow it to dry.
You have just made a model of the jaw and a tooth root. The concrete in the bucket is the bone of the jaw, and the drilled hole is the tooth socket. The cement inside is the tooth root, and the epoxy glue is the periodontal ligament that "glues" the tooth in place. Without the ligament, the tooth would probably fall out. With the ligament, the tooth can withstand all of the biting, tearing and chewing that animals do with their teeth.
Periodontal disease is the destruction of this ligament, the bone around the tooth, and the gums (gingiva). If the teeth are not brushed every day, bacteria move into the space between the edge of the gums and the tooth and take up residence. This is the area that flossing is supposed to clean. The bacteria and accumulating tartar together cause an inflammatory reaction (gingivitis). Eventually the bacterial infection and inflammation make the gum detach from the root of the tooth, forming a deeper and deeper pocket, much to the delight of the bacteria.
After some time, the ligament that holds the tooth in the socket is eaten away. The bone surrounding the tooth is lost as bacteria invade, and the tooth loosens and may fall out. Amazingly, we have seen pockets reach depths of 10-15 mm (over half an inch).