There are a lot of big Routers throughout the world. Often referred to as the Backbone. Basically it's a lot of routers connected to each other. Cables run from those massive routers to smaller routers owned by the ISP's. There they probably split it again a couple of times, depending on how big a region they want to connect.
So basically it's just networks within networks within networks etc and there's not a single monstrous machine in the middle. I think that's a good thing, because the owner of that machine would have the possibility to hold the world hostage or maybe edit data.
I'm not 100% sure about all this, but this is how it was explained to me.
