The Korean War, which began in 1950, was not a case of South Korea invading North Korea, but rather a result of an invasion by North Korea into South Korea.
In the years leading up to the Korean War, the Korean Peninsula had been divided into two separate countries: North Korea, which was aligned with the Soviet Union, and South Korea, which was supported by the United States. On June 25, 1950, North Korean forces invaded South Korea, with the aim of reunifying the country under communist rule.
The United States and other countries intervened on behalf of South Korea, and a United Nations coalition was formed to push back against the North Korean invasion. The war lasted for three years, until a ceasefire was declared in 1953, and the two Koreas remained divided along the 38th parallel.
The Korean War was a major conflict of the Cold War, as the United States and its allies sought to contain the spread of communism. The conflict also had significant consequences for Korea, which remains divided to this day.