If you ask people in Taiwan, they will say they’re independent. If you ask China, they’ll say Taiwan belongs to China.
The short history version is basically like this: after the overthrowing of the last emperor and WW2, the Chinese civil war continued between the KMT political party and the Communist party. KMT basically lost and moved to which is Taiwan today and even the KMT now is no longer the controlling majority now (they have elections whereas mainland China does not).