Paul McInnes, the Lead Designer for Citizen has posted a nice, long write-up on Factions and how they work in the game on the official CZ boards. Here is a snippet:
What Exactly is a Faction?
Factions in CZ are a bit different to factions in other games so before we delve into the five ways of factions, let's cover some basic ground first.
A faction is a named large-scale social actor within the game world of CZ. Each faction has a headquarters, its own set of preferred hangouts and a cadre of NPC members and affiliates that offer PC members various services and rewards. The faction embodies a natural interest group within the social world of the game and behaves accordingly.
You can read the entire post at this link.