| Something is said to work "on the honor system" if there are no strict safeguards against abuse, i.e. you are expected to follow the rules because it's honorable, but nothing directly prevents you from breaking them. Typical examples are the anti-cheating policies in colleges and universities, as well as the public transportation systems in German cities, which have no gates or turnstiles that require a ticket to get through.
The advantage is obviously that those who want the rules to be followed don't have to implement an expensive enforcement infrastructure and those who are expected to follow the rules don't have to suffer constant annoying checks. The disadvantage is that many people care little about honor and break the rules anyway, especially in big faceless systems.
The result is that an honor system is usually combined with occasional random checks and (more or less) draconian punishment for people who are discovered to have broken the rules. Thus, even though you may get away with cheating a few times, you'll eventually get caught if you do it regularly, and the punishment negates the advantages you might have gained. | 
