One of the ways a character in Planescape may demonstrate their personal philosophy is by joining a faction that supports it. A faction is an organization founded on philosophical principles. They operate out of Sigil, the City of Doors, and have areas of influence accross the Planes.
A faction background contains the basic features that all faction members get, including skill training, tool training, language training, basic equipment, access to faction dormitories, secret faction areas, libraries, training facilities, records, etc. Each background also includes knowledge of the location of a portal to your faction's planar stronghold, and a key to that portal.
Furthermore, faction backgrounds add a feature absent in other backgrounds: a unique way to use Inspiration. Each faction background comes with an alternative way to use Inspiration, such as offering success on saves or unique abilities such as Sifting. This is because factions come with philosophical principles: characters adhering to a faction philosophy should be facing problems because of it, and when they do that, they get Inspiration that they can use on these unique abilities.
Having a faction background is not compulsory to be a member of that faction. One could easily be a member of the Harmonium who was a Soldier, or a Noble Xaositect, or a Hermit Guvner. Though your features would be different, you can use your faction-specific Inspiration ability. There may be some particular reason you don't have the typical faction features — a Noble Xaositect for instance, might not live in the Hive, while a Harmonium Soldier would rely more on the army she is a part of than the City Barracks.
The faction backgrounds are as follows:
|Triad of Order||Triad of Despair||Triad of the Self||Triad of the World||Triad of Independence|
|Harmonium||Bleak Cabal||Transcendent Order||Sign of One||Xaositects|
|Unity of Order||Doomguard||Fated||Athar||Free League|
|Mercykillers||Dust||Society of Sensation||Believers of the Source||Revolutionary League|
Option: The Factioneer
Having a background for each faction allows a lot of diversity in faction membership, but games that don't emphasize the factions as much may not need that diversity.
So instead, you may only be interested in ONE background for faction membership, to go along with your Entertainers and your Folk Heroes and your Urchins. For this, we have the Factioneer.
Skill Proficiencies: Insight, Persuasion
Language Proficiencies: Any two
Equipment: A book of faction teachings, a stack of pamphlets espousing faction recruitment slogans, a set of traveler's clothes including a faction badge sewn into them, and a belt pouch containing 10 gp.
You can depend on other members of your faction for housing, food, and basic supplies. You have access to your faction headquarters in Sigil, and also know the location of a portal to their planar headquarters (and you have a key to that portal).