So, a long time ago (in 1949), there was a big war happening in a place called China. The people who were in charge were called the Kuomintang or KMT and they were fighting against another group called the Communists.
The KMT lost the war and they had to run away from China to a new place called Taiwan. It was kind of like when you play a game and your team loses, so you have to go back to your house and try again later.
When the KMT got to Taiwan, they set up a new government and started to run things there. They didn't want to be part of China anymore, so they began to act like their own country.
That's basically what happened, the KMT lost the war and had to move to Taiwan and start a new government there.