CESN says:
Just noticed that I’m not briefly sure what the affiliation means... in game terms. So the crew answers to a faction, the patron is an NPC but our PCs are part of something else? How does that work?
"Faction Affiliation" just refers to which faction you are an official, card-carrying member of.
Being a member of a faction is mostly for roleplaying. The benefits of joining a faction are that you
might gain access to certain restricted resources, such as faction-specific technology. You also need to be in a faction to take the
Faction Standing talent.
The drawback to being in a faction is that you have rules or people to answer to, in addition to your patron. And you sometimes have to deal with your faction’s politics.
Some people are really devoted to their factions. Other people are faction members in name only (meaning they do the bare minimum to maintain their membership, but otherwise don’t get involved in faction politics or daily faction activities). Obviously, you can also work for a faction while not being a member of it.
So in short, your character can take his or her faction membership as seriously as you want.
Hope that helps.