very simplified TLDR - Taiwan was in the UN as the representative of China and blocked People's Republic of China until 1970s when second and third world countries voted PRC in instead of Taiwan and now PRC as the representative of China blocks Taiwan https://en.wikipedia.org/wiki/China_and_the_United_Nations

fun fact, because USSR was boycotting the UN over this issue in the 50s there was no one left to veto US's intervention in Korea, therefore it was okay by UNSC