In Planescape, characters derive their power from their convictions, and people with similar convictions have banded together into planar factions to advance their cause across the multiverse. Because belief is power in a Planescape game, not only do these factions shape the classes, backgrounds, and feats that a character might have, but they directly empower the character….much like a magic item does.
Thus, a character who is a member of a faction in PS can attune to that faction as if it was a magic item, under certain circumstances, and gain an explicit magical benefit for doing so.
Attuning to a faction depends on one's rank and renown within the faction. Even chaotic factions have a certain measure of familiarity and expertise with their beliefs that this measures. Renown can be gained by undertaking faction-specific missions that advance the faction cause, and by that, you can gain further ranks. Each rank typically comes with one attunement option. When you attune to your faction, you select one of the options available to you. You can attune to your faction multiple times, each time choosing one of the abilities granted to you.
For instance, an Anarchist Factor with a Renown of 9 can attune to the Revolutionary League and pick one of the three abilities her rank and renown give her access to. That same character could use the three attunment slots they have to gain all three abilities. If that character later found a magic sword, they might un-attune from the faction and attune to the magic sword, but retain the other two faction abilities.
When you join a faction, your renown with them is 1 - you are considered to have done SOMETHING to prove your worth and loyalty to their ideas (typically, your initiation). Gaining higher renown entails taking faction-specific quests. The higher your renown, the more ranks you'll achieve and the more abilities will be open for you to use.