Short answer
The router shares the internet connection between your devices and routes traffic between the local network and the outside world.
Router, modem and WiFi
In many homes, modem, router and WiFi access point are the same physical box. The modem connects to the provider, the router controls traffic and WiFi provides wireless access.
Private IP addresses
The router gives private IP addresses to devices using DHCP. It uses NAT to let all devices share the public IP address.
Security settings
Change default passwords, use WPA2 or WPA3, update firmware and turn off remote administration if you do not need it.
Common questions
Should I restart the router sometimes?
A restart can sometimes solve temporary problems, but recurring issues should be investigated.
Can the router affect my IP address?
Yes. When the router reconnects, the provider may sometimes assign a new public IP address.