One tiny server per thing you care about
Imagine you could snap your fingers and get a small, private server for each chat room, each document, each game match, each user. It holds that one thing's state in memory and on disk, handles its messages, and talks to its clients directly.
That's a Durable Object. You never provision it — saying its name is enough to summon it. There is only ever one of it in the world, so everyone who names the same thing reaches the same place.