A router is a small computer running its own software. That software handles the radio, the connection to your provider, and the rules that decide which traffic goes where. Like any software, it collects bugs — and manufacturers ship fixes as firmware updates.
Old firmware shows up in oddly specific ways: one device that keeps dropping, speeds that collapse after a few days of uptime, or a router that needs a nightly restart. These are usually memory leaks or radio bugs that a later release already fixed.
Firmware also carries security fixes. Routers sit directly on the public internet, so a known flaw is scanned for within days of being published. An unpatched router can be quietly used to spy on traffic or attack other machines.
Most modern routers update themselves overnight if the option is enabled. Older models need a manual download from the maker's support page and a five-minute upload through the admin screen.