The Korean War began when North Korea crossed the 38th parallel into South Korea. The Soviet Union and China supported North Korea while the United States supported South Korea.
It all took place in Korea. North Korea (RED) invaded South Korea (White). After North Korea's invasion, the United States fought them back into North Korea where China supported. This ended up as a stalemate.
The Korean War began on June 25, 1950. It began when Kim II-sung lead North Korea into South Korea.
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After a while, both sides of the conflict were ready to end the war. The armistice was signed on July 23, 1953. They agreed that the POW got to decide if they wanted to stay or return to their home countries.