Dead Orbit wants humanity to colonize the stars instead of hiding under a broken god.
Future War Cult is always trying to research weapons that they can use to have an advantage in war which according to them is the only constant.
New Monarchy… idk something about royalty and wearing fancy clothes?
Yeah. They were a minor deal in Destiny 1, and existed for a short while when Destiny 2 launched but now mean nothing.
Back in D1, you could pledge to a faction and get faction specific rewards (armor and weapons) styled in the colors of that faction. Dead Orbit was black, white, and gray. Future War Cult (FWC) was blue, red, and yellow. And New Monarchy was red and white.
You’d rank up for a faction by wearing their class item while doing missions, strikes, or crucible. Or by doing that faction’s bounties.
Ultimately, not an important source of progression (they’d never gear you up to raid level) but it was a fun way to show community.