Routers route packets. They take the information you want to send and try to send it on to the right place.
This invariably means another router. Which routes them to other routers. Which routes them to other routers. And eventually, they are routed to their destination (e.g. Facebook or whatever). At the destination, their routers route them to the right datacentre, to the right server rack, to the right server, and so on.
Your home router is just the only thing in your house that “knows how” to send things to the Internet and get them back to you. It is the “default route” for your home, to talk to the wider world. All of your home router’s routes likely lead to your ISP and then the ISP routers route them out to the rest of the world. The only exception would be if you have something unusual like a 4G failover or a load-balancing multiple connection, where the “best route” for one particular packet of information might be to go one way, rather than the other (e.g. if the Facebook server is “nearer” the 4G connection or “nearer” your landline connection).
Your home router is no different to a business router which is really no different to routers in the ISPs or across the world. The only real differences are what technology they use to actually send packets (e.g. DSL, 4G, Ethernet, fibre, etc.) and how much data they are designed to handle and how much they are used to do unusual things to that data.
There’s nothing stopping you having multiple routers, or a router directly connected to the Internet in some fashion, it’s just incredibly unusual to do so and expensive. Generally, most consumers and businesses go through an ISP but some large organisations (e.g. Facebook, etc.) will have their own connection (“peering”) to other large places.
But they will have routers, just a bigger, more expensive, more powerful kind, that probably “routes” packets over fibre or other technologies. You have a home router that routes things mainly to your ISP, and probably only ever over DSL copper lines. But all your computers know what their “route” to the Internet is… the default route is listed in your computer’s network settings, and it’ll be the home router you have. The home router’s default route will be to your ISP. Your ISP will be managing dozens or even thousands of individual routes that go to destinations all over the world – satellite connection, undersea fibres, etc. And the routes for all of those will come to, say, the other end of the undersea fibre where there will be another router that knows where everything else is, and then go through another router and another as it follows the route it’s been given.
Look on your computer settings. You will find your computer’s “default route”. It’ll be your home router.
Look into the traceroute command, it’ll show you the route taken to reach any particular website from your computer. The first hop on that will be your home router, then your ISP routers then a huge number of routers all around the world, all trying to get your packet to the right place one step at a time, getting closer each time.
You are not connected “to the Internet” any differently to anyone else, the only difference is that your router only knows “The Internet is over that way”, it doesn’t know where Facebook is or how to get to it. It just knows to send it towards the ISP and that the ISP knows how to get it to Facebook. Your ISP, though, have a complicated peering arrangement which means it knows how to find all the places in the world that it needs to, and what the best route is to get to them all. Something that your router doesn’t need and probably doesn’t have (though some business routers do have those settings visible to you, e.g. BGP routing).
All your home router knows is that the ISP is saying “I can talk to anywhere, just send me the packets”, so that you don’t have to have multiple, and world-wide geographically disparate, and many different technologies to talk to all those places. You just let the ISP do it for you.
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