This could be caused by an injury, an infection, or some internal problem at the base of the nail. Dogs whose nails are on the long side may get them caught in carpet loops and pull or split them; the dewclaws (smaller nails on the sides of the paws) may get injured by branches or other objects the dog walks over or through. Any nail base could get injured if your dog stepped on  the wrong thing. Infections can be of different kinds that require different treatments. Masses as the base of the nail can also create problems.

 If your dog continues to lick and bite this area, you should have him examined by your veterinarian to determine a) the cause of the problem and b)the best way to treat it.