Your router almost certainly uses a DHCP server to hand out LAN addresses to the devices on your LAN, and possibly you have configured that yourself so that specific devices (often printers) have fixed addresses.
But the need(*) for the static address that Richard asked about is so that the outside world can send traffic to your modem/router, which has an address inside your ISP's network. Does THAT address ever change?
* - there are ways around this. Some people use public internet services that save their current WAN (ie public) IP address for them. Whenever someone sees that their public IP address has changed they log in to that service & update the stored information. Anyone (or anyone's app) that wants to access their system first queries the stored info, then sends their traffic to that address. Google for "dynamic DNS", DDNS etc.