Bunmei-kaika is a very long word that means a very important thing that happened a long time ago in Japan. Imagine you are playing with your toys, and suddenly your parents tell you that you have to learn a new way of playing with them. That's similar to what happened in Japan during bunmei-kaika.
Before bunmei-kaika, Japan was a country with many rules and traditions that were very important to people. But some foreigners, people from other countries, came to Japan, and they showed the Japanese people some new things. These new things included machines and ideas about how to do things differently.
The Japanese leaders saw all these new things and realized that Japan had to change. So they made new rules that allowed people to learn, travel, and do business in new ways. They also made new laws that helped to make the country more modern and to make life better for everyone.
So, in a way, bunmei-kaika means that Japan learned new things and became a more modern country. Just like how you learn new things and grow every day.