The primary focus of behaviorism and behavioral theory in philosophy is to deal with what can be observed. The founder of psychological behaviorism, John B. Watson, believed that psychologists should not study internal thinking processes because those can't be observed, and he criticized other psychological theories that focused on the unobservable, because he considered them less scientific.
A core belief in behaviorism is that behavior can be described and explained without using references to internal or mental processes. Behaviorists believe that people behave the way they do because of a complex set of external stimuli, which can be studied and observed. For example, a behaviorist studying a misbehaving child would look at how the parents treat him, how the parents reward him to encourage good behavior, and how they punish him to discourage bad behavior.
Because behavior is the result of external stimuli, behaviorists believe that behavior can be modified through the use of reinforcements and punishments. Reinforcements are stimuli that encourage a person to do the behavior again, while punishments discourage the behavior. For example, preventing your child from using the computer when he breaks curfew would be considered a punishment because you want the behavior of breaking curfew to stop. Behavior modification through reinforcement and punishment is called operant conditioning.
There are three major branches of behaviorism, and each takes a somewhat different angle on the central ideas in behaviorism. Methodological behaviorism holds that only a person's actions should be studied. Psychological behaviorism says that a person's observable behaviors, and the way those behaviors are linked to previous exposure to stimuli should be studied. Analytical behaviorists believe that a person's internal thoughts are directly linked to his behavior, and that his behavior will help predict his thoughts.