Theodore Roosevelt won the Nobel Peace Prize in 1906, while he was President of the United States. He won it mainly for his efforts to end the war between Russia and Japan that is known as the Russo-Japanese War. This is somewhat ironic because he is known as an aggressive president who was willing to use America's military might to get its way.
In 1905, Roosevelt invited both Japan and Russia to send delegates to the United States where he would mediate between the to try to find a way to end the war. Roosevelt wanted to do this largely because he believed that great powers like Russia and Japan should each have their own "spheres of influence" and that they should not try to take pieces of those spheres from others.
Because he successfully helped the Japanese and Russians to negotiate the end to their war, he won the Nobel Peace Prize.