Unassigned at IANA since 2007, and in practice the most common overflow port for a second web server.
IANA de-registered port 81 in 2007 and lists it as Unassigned. What fills it is HTTP: a second web server or virtual host on a box where 80 is already taken, a management interface behind a reverse proxy, and above all the embedded web UIs of IP cameras, DVRs and consumer routers, which frequently expose their admin page here. Because those devices are numerous and often unpatched, port 81 sees heavy untargeted scanning. Anything found on it should be treated as an HTTP service and fingerprinted with a normal HTTP request.
Expose with care
Usually plain HTTP with no TLS, and very often a device admin interface; put it behind TLS and authentication or do not expose it at all.
$ curl -sSI --max-time 5 http://TARGET:81/Seen this on your network? Beige Box scans your Wi-Fi and shows every open port on every device — and its Ports tool links straight back here.
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Corrections or a missing port? Reply @rimrocksystems.