Minority influence occurs when a smaller group over time is able to persuade the majority to join their side. A type of social influence, this topic was researched in depth by Moscovici. Minority influence uses conversion as a means for the minority group to be influential- conversion is convincing someone who originally doesn't agree with your views that you are right.
Examples of minority influence include the Suffragette and Civil Rights movements in the United States. These originated within a smaller group who over time were able to convince the majority to sympathize and agree with their side.