Avoidance learning is a behaviorist term that describes when an organism learns a response in order to avoid experiencing an unpleasant stimulus. The reinforcement (desired, pleasant result) results from not experiencing the negative stimulus (or punishment).
For example, in a lab a mouse hears a tone which is followed by a non-harmful but unpleasant shock. This shock is the unpleasant stimulus. The mouse can escape the shock by running through a little door. Eventually the mouse will learn to use the door once it hears the tone avoiding the electric shock altogether. This is avoidance learning- the mouse has learned how to avoid the unpleasant stimulus. A human example would be a person who gets an allergic reaction from eating a certain food a few times. Eventually they learn to avoid that food and not eat it at all. This is avoidance learning.