A number of citizens, whether amounting to a majority or a minority of the whole, who are united and actuated by some common impulse of passion, or of interest, adversed to the rights of other citizens, or to the permanent and aggregate interests of the community.
n. A group of people who express a shared belief or opinion different from people who are not part of the group. Usually the people in this group do not let others in unless they can somehow prove that they share similar interests and/or beliefs
One example of factions is all of the high school subcultures eg. Preppies, Nerds, Jocks, Bullies, Townies, Hackers etc.