In terms of a home network: A router is the device that allows your home devices to be connected to one another and route to the internet! It typically serves the Wi-Fi out to your wireless devices, but it is also where you would plug the ethernet cords into if you were hardwired. Most home networks have just one device that functions as BOTH the router and the modem at the same time, so you don’t have to worry about confusing the two. If you have an advanced setup, you might have your own or separate router.
It’s not only a good practice, but a must in today’s world: you should change the default admin password on your router so that bad guys can’t take control over your router.
