Most routers are actually small PCs, just optimized for the specific purpose of connecting to the internet over a phone or TV line, providing a separate internal network in your home and bridging the two. But you could do that with any regular PC with the right hardware.

Your ISP could also just provide you with a standard network connection, so you don't have to use a modem to transmit data over a line that was originally built for a different purpose. This is not very common since most houses still predate the internet, but it might become the norm at some point.

The main benefit of having a separate network is that devices in it are not directly visible and accessible from outside. All others see is your router, and they can only access your devices if you establish the connection first or manually forward ports. You can also structure the local network however you like (e.g. assign IPs and domain names, create subnets), without being restricted by or affecting the outside world.