Bayek isn't the only troublemaker in Assassin's Creed Origins. While traveling the city streets and country roads of ancient Egypt, he'll pass by groups of characters who have their own agendas, and their chief concern is often fighting other NPCs. It's like how rival gang members start scrapping in GTA, or even Assassin's Creed: Syndicate, but with more people and horses and spears.
“There are quite a few different factions in the world, and keep in mind that these factions are really living in the world,” creative director Ashraf Ismail says. “We don’t have anything that is a spawned event, you know, ‘because you’re 50 metres away we’re going to spawn this fight here for you.’ These are NPCs that have a schedule, that have an agenda, that criss-cross paths, and if they happen to be enemies they’ll fight, if they happen to be allies they’ll hug each other. So this is really the world living.”
So who will you meet on the road? At this point we know about three factions: the Rebels, who Bayek frequently works alongside; the Ptolemies, who are basically Egyptian enforcers, collecting taxes and taking prisoners; and the Bandits, who steal and pillage and generally do Bandit-y things. They don't really get along with each other.
You're free to join in when you see a skirmish unfolding on the horizon - it's a good way to try out the flexible new combat system - or you could just send out your eagle buddy Senu to get a bird's eye view of the fight. Wait until the fight is over and booby trap the bodies with lethal poison to give looters a nasty surprise.