When people talk about South Korea, they are often referring to the entirety of the Korean Peninsula. People have been living on the Korean Peninsula for thousands of years. It is difficult to say exactly when people first started arriving, but tens of thousands of years ago, the history of China and the history of Korea began to split. Therefore, even though people have been living on the Korean Peninsula for thousands of years, it is still seen as an extension of China itself. Today, South Korea is separated from China by North Korea, but the two Koreas were connected for the vast majority of their history.
Even though the Korean Peninsula is free today, its history has been one of conquest. For a long time, Korea was under the control of different countries. Throughout its history, it has been controlled by both China and Japan. Most recently, Japan controlled Korea during WWII. When Japan invaded China in the 1930s, Japan also took control of Korea. Eventually, South Korea and North Korea would both be freed by the United States when they defeated Japan at the end of WWII. In addition, hundreds of years ago, Korea was at one point controlled by the Chinese. Numerous other countries have tried to invade Korea at different points, but the country remains free in the modern era.
When Japan surrendered to the United States at the end of WWII, South Korea and North Korea were divided. Officially, the country was divided at the 38th parallel. North Korea was under the influence of the Soviet Union, which also had China under its influence as well. Then, South Korea was placed under the influence of the United States. Even though the division appeared to work well at first, it was obvious that it was not going to last. It did not take very long for the advancement of South Korea to outpace that of the North, and eventually, North Korea invaded South Korea, sparking the Korean War. Even though the history of South Korea formally begins with the end of World War Two, it begins in earnest at the end of the Korean War.
When North Korea invaded South Korea, it did not take them very long to push all the way to the very end of the peninsula. It also did not take very long for the United States to get involved. It knew that it had to set an example that the spread of Communism will not be tolerated, and that led to the Incheon offensive, beginning the involvement of the United States in the Korean War. Eventually, the United States pushed all the way through North Korea very close to the Yalu River, which is the border with China. Eventually, the Chinese pushed the United States back to the 38th parallel, leading to a ceasefire. That is why Korea is still divided to this day.
The country of South Korea is 75 years old, founded in the year 1948.