Software that is embedded inside your router. This software provides network protocols, security and administrative controls. When users install a router they access the firmware that is on a read-only memory chip inside inside the router to set up security and administrative options. Router firmware can be upgraded by the user.
See "Common Router Settings" in the Quick Reference section of Webopedia.
See also Webopedia's "Did You Know... Routers, Switches and Hubs: What's the Difference?"