What is "positive reinforcement" training?

Positive reinforcement means rewarding our pets for performing the behaviors we want. What constitutes a reward is determined by the individual animal. Many animals work well for food, but others enjoy working for toys/games or the opportunity to do something they enjoy.

Studies and practical experience prove that rewarding an animal when it performs the desired behavior increases the likelihood that the behavior will be performed again and again. (This is known as Thorndike's Law of Effect, which you can read more about by searching the web.) 

In training dogs, I take advantage of this effect to increase the frequency of behaviors I want, such as Sit, Down, Stay, etc. As the dog gets better at performing the behavior, the reward is slowly phased out until the dog will perform the behavior without necessarily having the promise of a reward every time. I still occasionally provide rewards, even if it's just petting, play or praise so that the dog continues to listen. We don't work at our jobs for free (or at least, not for long) and the same goes for our dogs.