You will start with your shelter acting as an outpost of sorts, providing control of your starting zone.
Other factions will control all other territories at the game start and these can be attacked to claim the territory for your own faction. These outpost fights are usually a bit tougher than the rest so keep the regions difficulty in mind when invading areas.
The main advantages doing so right now is the loot gained from the fight but it also means your parties travelling through the region will no longer be stopped by faction patrols. This is especially useful when using workable sites.
Allying with a faction treats its territory as your own: you will not get attacked by that faction any more.
Other factions may attack outposts you control.