Why Does My Dog Paw My Arm

I've recently had a couple of requests for some insight into a very common dog behavior--one my own Shadow-Pup indulges (see picture above). That is, why does my dog paw my arm? Here are two requests...and then we'll get into the reasons behind the behavior.

AMY SHOJAI'S Bling, Bitches & Blood - Practical Solutions for Pets Problems & Publishing