The main reason dogs lick feet is as a way for them to communicate status and deference to an owner. This is the same reason they lick a person's face or arm.
Since dogs cannot talk, they use their tongue as a way to communicate with their owners. Licking generally means the dog is showing submission and searching for attention from the person the dog sees as above it in standing. A second reason for licking a person's feet is as a way to gather information. Dogs have millions of scent receptors in their noses and mouths, and they use their tongue to process the rather unique scents of a person's feet.