Item Factions provide you different ways to obtain items, and you get the option to align with one of them for the first time during Chapter 9 of the campaign.
These two Item Factions let you choose to either enable trading with other players, or to improve your ability to find more and better items. While you can only be aligned with one Item Faction at a time, it is not a permanent decision and you can choose to switch your alignment. More information can be found from Factions Window (bound to Y by default).
Aligning with the Merchant's Guild enables trading with other players through the Bazaar and aligning with the Circle of Fortune enhances item drops and allows you to seek powerful Prophecies from the Observatory to help find more and better items.
There are restrictions to equipping items depending which Factions’ services were used to obtain them. For example, many items found while aligned with Circle of Fortune will require the player to be aligned with Circle of Fortune to equip them. Similarly, when an item is traded within Merchant’s Guild, no player aligned with Circle of Fortune will be able to equip it.
While aligned with either Faction and slaying enemies or completing quests you gain a resource called Favor. You then expend Favor to use that Faction’s services and gain Reputation, which is your experience with a Faction. As your Reputation grows, you will gain Ranks within the Faction which unlocks better benefits and rewards within the Faction. Reputation is also gained from experience. The total Reputation gain is equal between the Factions if all Favor is spent, and roughly half of the Reputation comes from spending Favor while the other half comes from just gaining experience.
Faction progress is shared stash-wide, which means that any character that has access to a stash with a character that has any Faction progress, will also share that progress. Once a Season ends, all Item Faction progress is moved to the Legacy environment, keeping the progress from the further progression.
After you have aligned with an Item Faction with one character, future characters sharing that stash are able to align with a Faction in the first town during Chapter 1, retaining the ranks you’ve gained with that Faction from previous character(s).