Nestorius didn’t like the idea that Jesus was both a man and a god at the same time. Nestorius thought that couldn’t really be possible. So he thought that Jesus must really have been two separate beings – a human one and a god one – at the same time, wrapped up together. They must have been different, but almost the same. But this was too close to Arianism for a lot of people.
Many Christians agreed with Nestorius. But the majority wanted to believe that Jesus could be both a man and a god. After a lot of arguing and a fair number of riots and street fights over who was right, official Church councils in both 431 and 451 declared that Nestorius was wrong. Nestorius himself died in 450, but his followers – Nestorians – still kept on believing that Jesus was two separate beings. Many Nestorians left the Roman Empire after 451. Most of them moved to the Sassanian Empire, where they were more successful. By 500 AD most Christians in the Sassanian Empire were Nestorians or Manichaeans, or both.
Nestorian Christians moved further east, too, and convinced many people along the Silk Road and into India and China to become Nestorian Christians too (though other eastern Christians were Manichaean). In the Middle Ages, there were Nestorian Christians in India, in Kazakhstan, in Mongolia, and in western China. But by about 1400 AD, there were not really any Nestorians left except in India. Most of the Nestorians became Buddhists or Muslims.