Jimmy Carter, who had been President of the United States from 1977 to 1981, won the Nobel Peace Prize in 2002. He did not win it for any specific act but rather for the sum of his efforts to promote democracy and human rights around the world.
As president, for example, Carter was instrumental in getting the countries of Israel and Egypt to sign a peace treaty. This treaty, known as the Camp David Peace Accords, was the first step towards creating a more stable and peaceful situation between Israel and its neighbors (this process has, sadly, not continued to work).
Since his term as president, Carter has been involved in many humanitarian and pro-democracy efforts. He often heads groups that mediate conflicts or that observe elections to try to ensure their fairness. He founded the Carter Center which is meant to try to promote democracy and and to generally improve the lives of people in poor countries.
For all of these actions, Carter won the Nobel Peace Prize in 2002.