The Korean War was a major civil war on the Korean peninsula soon after World War II (see Pacific War). It became a significant engagement for both the United States (leading the United Nations forces) and the People's Republic of China. The resulting stalemate divided the country and a people by creating the nations of North Korea and South Korea.
After Japan's defeat at the end of World War II, the Korean nation was liberated but soon became divided by the ideological struggle starting the Cold War between the Soviet Union and the United States. Kim Il-sung established a communist regime with the support of the Soviet Union in the North, while Syngman Rhee established a capitalist regime with the support of the United States in the South. The North and South governments both claimed authority over the entire peninsula, and antagonism from both sides eventually led to an invasion of the Southern part by the North.
The United States military returned to support the South Korean forces, but the prospect of American troops on the Chinese border led to a counter invasion by massive Chinese reinforcements. The war lasted three years and saw the capital Seoul change hands no less than 4 times.
The result was a stalemate and the country was cleanly cut in half, with the Communist North and Capitalist South developing into the two extremely different nations they are today. Although there has been relatively little violence since the armistice, there has been very little progress toward concluding a peace treaty in the decades since.
Korea is rather unique in having an officially active war zone that you are able to visit. The Demilitarized Zone has been on edge for over 50 years and shows no sign of ending. Although the two Koreas remain technically at war with each other, and there have been military skirmishes (and deaths) over the years, there has been nothing resulting in a resumption of open warfare.