Game concept
Faction
The game also links it as Factions.
From the game's encyclopedia
A Faction is a group of Vassals with common political interests. The local population of Counties can also join certain types of Factions, such as the Peasant Faction.
Factions become dangerous once their Discontent reaches a certain point, at which time they will issue an ultimatum.
The game's text for patch 1.20.1.2. Words in blue are entries of the encyclopedia: hover one to read it, as in the game.
Faction is an entry of Crusader Kings III's in-game encyclopedia. The game explains it: "A Faction is a group of Vassals with common political interests." It covers Independence Faction, Liberty Faction, Claimant Faction, Ceremonial Claimant Faction, Peasant Faction and 7 more. The game also links it as Factions. Patch 1.20.1.2, from game/common/game_concepts/00_game_concepts.txt and game/localization/english/game_concepts_l_english.yml.
Source: game/common/game_concepts/00_game_concepts.txt, game/localization/english/game_concepts_l_english.yml and the English localisation, Crusader Kings III 1.20.1.2.