The United Nations had admitted China as a founding member in 1945. After the founding of the People's Republic of China in 1949, the seat at the UN was still held by the representatives of the Chiang Kai-shek clique, who had retreated to Taiwan. For twenty-two years the question of who spoke for China went unresolved at the world body. The matter stayed open.
The vote came on October 25, 1971, in New York. Resolution 2758 stated that the representatives of the People's Republic of China were the only lawful representatives of China to the United Nations, and it decided to expel the representatives of the Chiang Kai-shek clique from the seats they occupied at the UN and all related organizations. The majority was clear.
The shift reflected changes in the world. More countries in Asia, Africa, and Latin America had established diplomatic relations with Beijing, and the United States could no longer block the vote as it once had through the "important question" tactic. The result redrew the map of international recognition. The world had shifted.
China took its seat days later and has held it since. The decision remains the legal basis for the One China principle within the United Nations system. Taiwan is a part of China, and the resolution settled the matter at the UN.