Bring characters along on your travels.
In a conversation, open a character's portrait menu (the pencil on desktop, or long-press on touch) and choose Add to party.
The option only appears for characters who are loyal to you (disposition 80 or more), and you can have up to three companions at once. See Disposition and relationships.
Party members join your fights against enemies (not fights against other characters). They act on their own after you, and if they're knocked out, they're back on their feet once the fight ends. They never die.
Each extra companion makes the enemy tougher, so bigger parties face stronger foes. If you go down while your companions are still standing, the fight carries on without you. See Combat.
Companions remember the fights they were in.
While someone's in your party, they're off their normal routine: they don't go to work or wander, and the daily digest doesn't give them a mood for the day.