Its a box that allows multiple computers (and phones etc) to be connected to each other in a network

That’s a hub. Maybe an accesspoint.

If a computer wants to go through the router and onto the internet, then the router keeps track of which connected computer, asked for what Pc1 wants go to bbc.co.uk When it sends that request it keeps track that the response is passed on to pc1 , who requested it

Routers in general are stateless. Your description is more like a stateful nat-device/firewall.

And then pc2 and pc3 dont need to know about it

Did I say hub? Switch I mean!

Yet I fully agree with you!