The extra "fingers" on a dog, higher up on the inside of the leg than his other claws, are called dewclaws. These appendages are vestigial -- they no longer serve the purpose they once did at some point in the development of canine species. All breeds of dogs have front dewclaws, and some dogs have back dewclaws and even multiple back dewclaws. For some active breeds, dewclaws may be a nuisance and removal may be appropriate.
All dogs have two front dewclaws, one on the inside of each front leg near the foot. The dewclaws are often attached by bone and tissue; they are not dead. Some dogs will use their dewclaws to help grip bones or to gain traction when they run. Some unique breeds, including the Catahoula leopard dog, the Basenji and the New Guinea singing dog, use their dew claws to climb trees like a cat.
The nails on the dewclaw grow just like the other nails, so they need regular trimming; otherwise the nails might grow into the pads. Occasionally, a dog may get the front dewclaw caught on something and cause an injury. Other than that, most dogs never have any issues with their front dewclaws.
Back dewclaws aren't nearly as common as front dewclaws. Usually, these extra digits loosely connect by just a flap of skin, so they can get caught easily. Many owners choose to have the rear dewclaws removed to keep them from getting snagged or torn.
Some breeders remove the dewclaws when pups are just a few days old -- your pooch may have had a rear dewclaw when he was born, and you never knew. Some owners elect to have the rear dewclaws removed to prevent injury, or in response to an injury. While the dewclaw isn't a necessary body part, removing it requires minor surgery and poses some risk from anesthesia, complications or potential post-operative infection. A declaw attached with tissue and bone requires more complicated surgery to remove.
Some breed standards include dewclaws for show dogs. The Briard, the Beauceron and the Great Pyrenees all require double dew claws on each back foot to meet the breed standard, while the Berger des Pyrenees and Saint Bernard require single rear dewclaws. The Norwegian Lundehund may have either single or double rear declaws. The declaws for these larger working breeds help provide stability when they are working in rough, mountainous terrain.