What exactly would a “stateless society” look like/how would it function?

u/JITTERdUdE - originally from r/GenZhou
I’ve been wondering lately how this would work, as I know the idea is that many institutions that are governed by the state would be run entirely by the people. However, I’m wondering how this would work. How would these institutions operate without a state? What does it mean to be run by the people? How is it any different from what anarchists envision?