Although I learned of the Happy Face Token System as an answer to prayer, there is psychological reason it works. Psychologists refer to this kind of reinforcement as A Token Economy. ―It is behavior modification based on the principles of operant conditioning. Contingency management systems are often employed by those who practice applied behavior analysis. Tokens themselves were not reinforcers; tokens were accumulated and "spent" in order to obtain a reinforcer. "Patients earn tokens, which they can exchange for privileges, such as time watching television or walks on the hospital grounds, by completing assigned duties (such as making their beds) or even just by engaging in appropriate conversations with others" (Nolen Hoeksema's Abnormal Psychology)
Positive reinforcement is an increase in the future frequency of a behavior due to the addition of a stimulus immediately following a response. Giving (or adding) food to a dog contingent on its sitting is an example of positive reinforcement (if this results in an increase in the future behavior of the dog sitting).
Negative reinforcement is an increase in the future frequency of a behavior when the consequence is the removal of an aversive stimulus. Turning off (or removing) an annoying song when a child asks their parent is an example of negative reinforcement (if this results in an increase in asking behavior of the child in the future). Courtesy of Wikipedia