When you protest peacefully or work for social changes without resorting to violence, that's nonviolence. Two of the most famous proponents of nonviolence were Gandhi and Martin Luther King, Jr.
Nonviolence is a principle, a personal value system, or a way of life. People who practice nonviolence live their lives harming as few other people (or animals, often) as possible. Many political protesters use nonviolence as a tactic during demonstrations, such as sit-ins, die-ins, and other forms of civil disobedience. Once Gandhi used the word nonviolence in this way in 1920, the word became associated with social and political activism.