The Korean War was an attempt by the Northan to annex the South, but also a test by Joseph Stalin of the resolve of the World South Korea remans and no general world war occured inthe 1950s1950s.
Explanation:
The end of the Second World was sawe Korea more or less arbitrarily divided along the 38th38th Parallel between the US and the Soviets. Stalin, as he did in Europe, used the opportunity to establish a satellite state in North Korea under his influence. The Americans -- more interested in getting their troops home - left a constabulary force and encouraged South korea to stabilize and become more modernized.
Kim IIII Sung, stalin's client, hoped to forcibly unite Korea; and by 19481948 sensed his own military was greatly superior to that of South Korea and the US Constabulary Force. Stalin wanted to see if rest of the World was too weary after the Second World war to stand up to aggression, and also wanted to be in easy reach of Japan (Russia and Japan had fought each other four times between 19051905 and 19451945).
The initial North Korean invasion of June 19501950 went very well, capturing almost all of South Korea in a few weeks, but then the Americans (with help from UN member states) mounted an amphibious landing at Inchon and by November had over-run almost all of North Korea. This resulted in a Chinese intervention, but by the Spring of 19511951, the frontlines had more or less stabilized along the current North-South Korean border.
The Chinese and what was left of the North Korean military (backed with Soviet equipment and supplies ) didn't have the strength to overrun the south again, while the UN allies feared an escalation of the war if they got up to the frontiers of China again. The deadlock remained while the Pyongyang talks went on for two years; largely because the Russians and the Chinese continued to test the resolve of South korea and its Allies to continue the conflict.
Stalin's death in early 19531953 and the continuing resolve to defend South Korea brought an armistice -- although North Korea has yet to formally agree to an end of the conflict. Only now, is Kim IIII Sung's grandson, Kim Jung On, showing signs of actually recognizing formal existence of South Korea.