That's a very good question, and sadly the causes could be one or more of several.
Some dogs are very clean, and especially if they have fluffy feet, the groom, almost like a cat, to keep their feet, especially between the toes and pads clean. In these animals the skin is usually normal and there is not brown saliva staining of the fur.
Others deal with conditions similar to athletes foot, only it tends to be a bacteria (can be yeast) and it is not contagious as with athletes foot in people. These dogs will lick vigorously and the skin is often red and puffy and may have a rash or even little abscesses. Sometimes topical antiinflammatories can work (powders or hydrocortisone type ointments) but this can be messy and difficult to do, and takes constant work.
Others (and there is overlap) have allergies or sensitivities to things in the environment (grass, weeds, leaf dander, carpet fresheners, carpet fibers, cleaners) and they actually have an allergic issue between their toes that causes the itching/licking. These will often get the infection mentioned above, but the primary problem is the itch and the infection is usually second.
Food allergies are also notorious for foot itching for whatever reason, and are not responsive to medicines.
With all that said, things we can do to limit this would include, washing or wiping their feet, with special attention to between toes and pads. Baby wipes or special antiyeast wipes for pets can be used, or just a gentle cleaning solution. This can help keep the feet clean and help limit the dog's desire to groom.
Topicals, as mentioned, can be a real pain, but some people will faithfully use them and they can help. They can also be messy.
Clipping long fur and keeping the feet groomed can help, but the act of grooming can irritate the feet so this can be a mixed bag.
Finally, your vet can often prescribe an antiinflammatory medicine if the problem is somewhat incessant. If they are keeping you up at night licking, limping or obsessing, or if the fur is stained brownish, these are indicators that maybe the problem is big enough to warrant and benefit from medicines.
I hope this helps sort out foot licking. If you have other questions or I can clarify something, please just write back.
Thanks!!!! ---- Dr. Will