Factions are entities that play an active role in galactic life and politics. They may be purely military, purely political, or both. Each civilisation, criminal group, and other such troupe of people are considered a faction. Primarily what separates a faction from an organisation is both their goal but also whether or not they're designed to make money as a business.
All players can join NPC factions provided they are able to mustre the requirements and curry favour. Player factions are created by the players themselves and joining those factions is something that the faction's creator is responsible for administering.