Brought up to care about other people
A Japanese person is usually brought up to care about other people. As this value is implemented in the minds of Japanese people they tend to respect others and maintain their promises.
It’s a cultural thing
Discipline is a part of the Japanese culture. Even a non-Japanese person who gets raised up in Japan can find it hard to not stick to the rules most people follow.
Their culture favors the community
The Japanese culture favors the community over the individual and as a result people tend to value discipline, harmony and all of the other things that could help the whole community live a better life.
A sense of shared responsibility
Japanese people have a strong sense of a shared responsibility. As a result of this way of thinking, they tend to feel very responsible for their environment, the place they live in and for others.
According to one theory, the fact that Japanese people live a tough environment where space is limited and lots of natural disasters happen has motivated them to be more coherent, organized and disciplined in order to survive. (See Why do Asians work very hard?)
The shinto principles
According to Wikipedia, Shinto is a popular religion in Japan. One of the concepts of Shinto, according to a Quora thread, is to do one’s best in regards to the task at hand. This could have helped shape the discipline of Japanese people.
They survived many natural disasters
The fact that Japanese people survived many natural disasters including the Hiroshema/Nagasaki bomb could have helped them learn how to become more organized and disciplined. (See Video Summary: 24 Hours After Hiroshima 2/3)
They respect authority
An important part of the Japanese culture is the deep faith and respect for authority. Those kinds of beliefs make Japanese people orderly and organized as they trust the rules set to them by others including the government and rulers.
The crowded Japan theory
According to one theory, the fact that some places in Japan are very crowded have taught people to become more orderly and organized in order to be able to finish things on time.
Their feelings towards laws
Japanese people think of laws as things that are guided and enforced by the people. As a result, people watch for law violations as they feel responsible towards making sure laws are not broken.