Contingency is the relationship between two events, one being "contingent" or a consequence of the other event. Behaviorism (ABA) sees all behavior as a response to an antecedent and driven by the consequences. All behaviors have a consequence, even if that relationship is not very clear either to the observer or the student who may be the focus of an intervention, either behavioral or instructional.
The goal of an Applied Behavior Analysis intervention is to change behavior. It may be to increase the desired behavior, to replace a problematic behavior or to extinguish a dangerous or difficult behavior. In order to increase the desired behavior, the student needs to know that receiving reinforcement is directly related to the behavior, or "contingent" on the behavior. This relationship of contingency is incredibly important to the success of an Applied Behavior Analysis program.
The success of establishing contingency requires quick reinforcement, clear communication, and consistency. Students who don't receive immediate reinforcement, or are not clear about the relationship of contingency, will not be as successful as those children who clearly understand the relationship or contingency.
Examples: It took a while for the team at Jonathon's school to help him understand the contingency between his behavior and receiving reinforcement, so they repeated a simple imitation program with direct, one to one reinforcement until he would comply regularly.