Why can many dogs easily learn this action? It is because during the nursing period, puppies press their front paws on the mother dog's teats to stimulate milk secretion. As they grow up, this action of raising the front paw to scratch is inherited as a gesture dogs use to request food or affection from their owners. And shaking hands just coincides perfectly with this action, so many dogs can easily learn this trick.

　　When you are enjoying a delicious meal, and the dog sitting beside you keeps wanting to shake hands with you, now you should understand, the dog is not just showing friendliness; it actually wants a share of your food. (Source: PetsZone)