Hansei (反省?, "self-reflection") is a central idea in Japanese culture. Its meaning is to acknowledge your own mistake and to pledge improvement. (Similar to the German proverb "Selbsterkenntnis ist der erste Schritt zur Besserung" where the closest translation would be "Self-awareness is the first step to improvement").
An example would be Japanese politicians involved in corruption. They appear in public and apologize, then disappear from politics for a few years. After some time they resume their career because it is thought they learned their lesson.
In Japanese companies it's common practice that a manager expects hansei from his subordinates in case of mistakes. The manager takes the blame in public, whereas the department works on solving the problem.
Hansei also means greeting success with modesty and humility. To stop hansei means to stop learning. With hansei one never becomes so convinced of one's own superiority that there is no more room or need for further improvement.