It’s a network topology as well as a family of networking protocols depending on how specific you wanna get.

The Internet as it stands is largely hierarchical in terms of bandwidth. We have the fiber backbone that runs along the bottom of the ocean and the upstream ISPs pull from there and the local ISPs pull from them and then we get our connections from the locals. So if you want to communicate with a server across the ocean (as must of us do every day whether we know it or not) your packets need to climb all the way back up the bandwidth hierarchy. That hierarchical model you can diagram out like a big branching star.

Mesh networks look more like spider webs with neighbors having direct connections to each other and making the resulting network have a lot of redundant connections which are resilient to outages. Imagine a world where if your ISP had an outage, you could still communicate with your neighbors via federated social media because your houses all have direct connections and each of them hosts a micro server with all their social data on it. This sort of thing could be very useful for emergencies and also much more censorship/surveillance-resistant