Korea used to be one big country, but then during World War II, the Allies (countries like the United States, United Kingdom, and China) were fighting against Japan, which had taken control of Korea. After the war, the Allies wanted to make sure Japan couldn't control Korea anymore, so they decided to divide it into two parts.
One of the two parts was called North Korea and was given to the Soviets (Russia). The other part was called South Korea and was given to the United States. The Soviets and Americans set up governments in both parts, but they ended up being very different. North Korea became a communist country where everyone had to follow the same rules, and South Korea became a democracy where people had freedom and could elect their own leaders.
To this day, the two countries are still divided, with North Korea still a communist country and South Korea still a democracy.