A system where they do not enforce the rules but people are expected to follow the rules. For example, a club provides drinks in their refrigerator. The drinks cost $2 and there is a box next to the fridge. If you take a drink, you should put $2 in the box. However, no one is there to check and if you take a drink and don't pay no one will know. It's an honour system which relies on trust not on force.

An honor system is a code of conduct where violation of rules is not tolerated, and all subscribers of the code are obligated to report infractions, including their own.

Here is one example of "honor system." There is a subway (metro) in my city. For many years, the honor system was used. That is, passengers were asked to buy tickets and then to board the subway trains. No one checked them to see whether or not they bought tickets. The honor system did not work. Many passengers did not buy tickets. So now there are gates at the entrance to the subway platform. If you want to proceed through the gate, you must prove that you bought a ticket.

Thank all of you. Those answers are helpful, especailly the one with an example.

This is from Wikipedia: An honor system or honesty system is a philosophical way of running a variety of endeavors based on trust, honor, and honesty. Something that operates under the rule of the "honor system" is usually something that does not have strictly enforced rules governing its principles. In British English, it would more often be called a "trust system." So you should probably either write "honor system" (no U) or "trust system," depending on whether you are in Shenzhen or Hong Kong.