But how this happened?

There are plenty of places in the world that have cheap labor and unlimited demographic resources, but only China could rise from outsourcing haven to something bigger.

India has same large population and even better starting position - no communism, better English language knowledge in population, open market economy and economical ties with UK. It has industry and science, but it is nothing compared to China. Eastern Europe (non-USSR part) started in same position as post-communist land, but still remains outsourcing haven for EU and nothing more, while having better educated people than China on average. Latin America struggles for years in constant growth/crisis cycles, also has no cultural and political restrictions as China, but overall it still undeveloped. USSR even had similar reforms (Perestroika) but it didn't help, and even now country is just an oil exporter and nothing more. Africa... oh, you all know.

Maybe first reason is a strong but adequate government. Top part of government decided to achieve the goal and had enough control to stop lower levels from failing it by corruption. Government also had no pressure from internal competitors, while in other countries it is more about "survive and win next elections, and who cares". But it couldn't be sole reason of course.

China also isn't a backwards country overall, it is country with thousands years of history, including imperial periods with large bureaucracy and half-religious legalism. It just had bad period in 18-20th centuries, but there were times when they were almost best in the world in development sense. Western historiography often ignores it because eurocentrism. And even communist disaster couldn't really destroy all thousand years of state legacy. Also it must be noticed that China is an Empire that didn't break, not a national state like European countries.