Reinforcement encourages behavior while punishment discourages it. Both develop learning through what is called operant conditioning, in which behaviors increase or decrease based on the type of result obtained.
Edward Thorndike was a psychologist who first studied operant conditioning, which describes the learning that is based on the consequences of the learner. His work influenced that of B.F. Skinner, a behavioral psychologist who developed the terms reinforcement and punishment in terms of operant conditioning. Skinner's work showed that punishments tend to decrease the likelihood of specific behaviors while reinforcements tend to increase the likelihood of specific behaviors.
Both terms can be described in positive and negative terms. Positive reinforcement offers something desirable to increase positive behaviors, while negative reinforcement removes something undesirable to increase positive behaviors. Positive punishment offers something undesirable to reduce negative behaviors, while negative punishment removes something desirable to reduce negative behaviors.