Majority influence occurs when the behaviors or beliefs of a larger (majority) group of individuals influences the behaviors or beliefs of a smaller group. This is a type of social influence in which conformity occurs.
A classic example in psychology are the studies by Solomon Asch in the 1950s. In his experiments participants were put in a room with other people that they were led to believe were other participants but were in fact confederates, which are experimenters pretending to be participants. When asked which line on a board was the longest the confederates would respond by choosing a line that wasn't the longest. This would frequently cause the real participant to choose the same line even though it clearly wasn't the longest.
Over the course of 12 trials the results showed that participants conformed to the majority influence of the confederates and chose the non-longest line over 75% of the time. This is an example of majority influence in that change occurred in an individual due to the influence of the larger group of people.
The opposing concept of majority influence is minority influence which is when the beliefs and actions of a smaller group socially influences the larger majority. An example of this is the US suffragette movement in the early 1900s in which the initial hard work of a small group resulted in women getting the right to vote.