The renewal effect is when a conditioned response (CR) behavior returns when a change of context or environment occurs after extinction. When a CR has been extinguished the organism no longer emits the behavior when the conditioned stimulus is presented. But when a change of context occurs the CR can come back as if it had never been extinguished.
Context are stimuli that are present in the organism's environment. The stimuli can be manipulated in a research capacity or simply be noise or visual stimuli in the background environment where the learning and conditioning occurred. The renewal effect is strongest when an organism is returned to the original context in which the extinguished behavior was learned.
An example is illustrated by an experiment with rats. A rat is inside a blue colored box and learns that it will receive food when it hears a tone. Eventually the rat will run to its food tray (CR) as soon as it hears the tone (which has become the conditioned stimulus). The rat is moved into a white box and is taught the same exact procedure. Eventually the researcher extinguishes the behavior by not providing food with the tone and the rat stops going to the food tray. If the renewal effect occurs the rat will start going to the tray when it hears the tone without the presentation of food. It is more likely for the CR to come back in the blue box which is the original context the rat learned the behavior.