Groups, organizations, clubs, societies, guilds, associations, parties, lobbies.
For this purpose of this discussion, we’ll just call them factions.
Factions are important for fictional worlds, just as they are in our own history and cultures. Whether political, social, religious, fraternal, or other factions, all have an influence on society, politics, and history. They can also be used to introduce depth, variety, and veracity to the fictional world.
For example, take the Catholic Church. On one hand, this is a monolithic entity that is supposedly united. Internally, though, the Church has many factions from monastic orders like the Cistercians and Franciscans, to priestly orders like the Jesuits, to lay organizations like Opus Dei. Each internal faction has its own interests, goals, and desires. This creates politicking within the overarching organization.
Historically, we like to say that nations were ruled by kings who had absolute power (in Europe, for example). However, a king who ignored the religious orders, trade or craft guilds, knightly orders (of which there were many), noble families, wealthy mercantile families, and other factions tended not to rule long or well.
Fantasy fiction is chock full of factions from orders and guilds of magicians to priests of different faiths to trade guilds and thieves guilds. We are familiar with many of these. What we don’t generally see are sub-factions. Some exceptions do exist, of course. George R.R. Martin started to get into factions, beyond the noble houses, with his discussion of militant religious orders in Westeros, various military groups in Daenerys’ army, and sub-divisions of the Nights Watch. J.K. Rowling gives a hint of factions in the various Ministry of Magic departments (loosely based on British ministries) and even the Hogwarts houses (orders of magic, guilds, fraternities?). Ilona Andrews demonstrates factions well in the Kate Daniels series, along with some sub-factions (particularly among the Pack), in the urban fantasy/post-apocalypse genre.
In sci-fi, I think one of the best examples, if not the best, is C.J. Cherryh. In both her mainline world (Downbelow Station, Merchanters Luck, Cyteen, etc.), she presents a highly factionalized world, even amongst the seemingly unified Cyteen government. Likewise, her Foreigner series presents noble families, guilds of various sorts, and other factions woven into a complex political and social web that leads to a great deal of the series’ tension and plots.
Obviously, there are other famous examples of factions in fiction, some of which have made an entire series or world famous: Starfleet, Jedi, Sith, UNIT, the Rangers (B5 or Tolkien), Psi Corps, the Peacekeepers, Stargate Command (& SG-1), Hogwarts School of Witchcraft and Wizardry, Xavier’s School for Gifted Youngsters, The Avengers, the Brotherhood of Mutants.
Whatever the faction, they should not be skipped over, even if supposedly trite and/or overused (thieves guilds). They form an important element of any world and suspension of disbelief.