The King Leopold II that you are referring to in this question was the King of Belgium. He reigned from 1865 until his death in 1909. He is connected to the Congo because he acquired that region as a personal holding (as opposed to a colony of the country of Belgium) and exploited it in a manner that was terribly brutal even for that time period.
In the late 1800s, a “scramble for Africa” occurred. This was a time during which European countries were trying to take as much of Africa as they could for themselves. At that time, people believed that countries needed to have empires in order to be strong and prosperous. Countries like France and the United Kingdom already had empires and other countries were trying to catch up to them.
Leopold believed in the need for colonies. Therefore, he tried to get various areas of the world for Belgium. However, he did not do this openly. Instead, he tried various ways to conceal what he was doing. By the mid-1880s, he was able to get the international community to assign the Congo to a company that he owned. It was disguised as a philanthropic organization. The international community gave the company control and the company claimed that it was going to try to improve the lives of the natives.
Instead, Leopold caused horrible atrocities to be committed in the Congo. He ran the colony in a brutal way, demanding that the natives work to make money for him (largely by producing rubber) and punishing them severely if they did not. His regime was so brutal that the international community was horrified. Pressure from the outside eventually forced Leopold to relinquish control of the Congo. He was no longer allowed to rule it personally, but was required to give control of it to the Belgian government.
Thus, we can see that King Leopold II of Belgium was closely connected to the history of the Congo.