If you're using an Apple Air Port router, you can use the Air Port Utility program to check for updates.
Your router’s firmware is basically the operating system that is specifically designed to run on your specific make and model of router (unless you are using a multi-router compatible open source firmware such as DD-WRT).
If you don’t update your firmware then you won’t be able to take advantage of any speed boosting upgrades that your router manufacturer might release in an update.
Every router is different, but usually, they have a similar process for upgrading the router’s firmware.
Here are the basic steps for performing a firmware upgrade, check your router manufacturer’s website for specific instructions for your make and model.
Most modern routers use web browser based administration which means you basically type in the IP address of your router in order to access it’s administrative functions.