The Korean Autonomous Province in northwest China exists to give, as the name suggests, Koreans autonomy.
As an additional question what led to the creation of this province and the emergence of the Korean majority in the region?
Historically, Korea covered not only the peninsula, but Manchuria (Liaoning, Jilin, and Helongjiang provinces) and Primorsky Krai, Russia. The Buyeo people controlled part of Manchuria, and they were absorbed into the Goguryeo, who controlled area further east, including the present-day location of Vladivostok. There were other, smaller Korean tribes that controlled parts of what is now China as well. So, historically, these areas were "Korean," whatever that means.
However, the "Koreans" that are living there now are mostly descendants of people who moved there over the past 150 years. In the later half of the 1800's, there were some natural disasters and, subsequently, general trouble in Korea and many people in the area moved across the Yalu and Tumen rivers. The Qing government began developing the area, which was devoid of people due to a ban that had been in place earlier. This development attracted more people from Korea and that's about it.
During the Japanese colonial era, Manchuria was akin to the Wild West - far away, lawless. Many Korean freedom fighters fled into Manchuria, including (amongst others) Kim Il-sung.
Just to be clear, people of Korean descent do NOT constitute a majority in the region these days. However, many Joseonjok (Chinese of Korean descent) in Korea come from the Northeast Provinces, and many Koreans who travel to China for tourism go to the Northeast provinces. The area is home to Baekdusan, the mountain from which the first Korean, Dangun, came from. There are also many examples of early Korean pagodas in the area, statues to Korean independence fighters have been erected (the most notable one is in Harbin, of An Jung-geun, the assassin of Ito Hirobumi), as well as the museum there regarding Unit 731, the Japanese unit that killed many local people, including local Koreans. IIRC, there are something like 600,000 Koreans in Yanbian now, and approximately 2 million in the Northeastern provinces all together, compared to 2 million people total in Yanbian, and around 120 million in the whole Northeast.
