During World War II, Japan occupied the nation of Korea. When Japan was defeated in 1945, the United Nations divided Korea at the 38th parallel, to be administered by the Soviet Union in the north and the United States in the south. This led to the establishment of separate governments — the Communist North and democratic South — but both claimed to be the legitimate government of all of Korea.
Disputes and military skirmishes at the border between the two nations became commonplace, and finally in 1950, North Korea invaded and seized Seoul, the South Korean capital. The United Nations, led by the United States, sent military forces to aid South Korea, and the Korean War was officially under way.
By 1953, after both sides had suffered substantial loss of life and after Seoul was captured and recaptured by North Korea and the United Nations several times over, the Korean War ended in a stalemate. The two sides agreed on a new border called the Korean Demilitarized Zone, which is a strip of land between two and three miles wide that separates the two countries. An official peace treaty was never signed, however, so technically the two Koreas have been at war with each other since 1950.
While other Communist nations collapsed and China found a way to balance a free market with Communist leadership, North Korea remains a totalitarian Communist nation. The North Koreans do not allow foreign journalists into the country, but various humanitarian groups have reported "severe repression" of the North Korean people (according to some reports, those who practice religion are subjected to torture, execution, or extremely harsh treatment in prisons and labor camps). Supposedly, the North Korean population also suffers frequent famine despite the wealth of its government.
In recent years, the North Korean government committed to a nuclear weapons program, causing U.S. President George W. Bush to list the North Koreans among the nations that made up his "Axis of Evil" and to call for sanctions against the nation. This caused North Korea to state its goal of building a nuclear missile that would reach the western shores of the United States.
In 2006, the North Koreans successfully tested an underground nuclear weapon. Despite signing an agreement with South Korea, the United States, Russia, China, and Japan to shut down its nuclear program in exchange for economic and energy assistance, in 2009 North Korea continued its nuclear program.
Even as its nuclear program continues, it remains unlikely that North Korea will ever really attack the United States. Doing so would be considered a declaration of war and the United States would certainly retaliate. But even the mere thought of one more nation having nukes that are capable of striking North America is more than the U.S. government is comfortable with, and in this age of terrorism, every nation with nuclear weapons increases the chances of these weapons being sold or stolen and/or disappearing across the borders of other nations.
It isn't out of the question that if North Korea continues to develop and test nuclear weapons, the United States will launch an offensive to destroy the missiles on their launch pads. But North Korea has made it clear that such an act would cause them to retaliate against South Korea.