An appliance in this context is a computer which can be stuck in an attic, nailed to a wall and forgotten about. If there is problems with it, you can power cycle it and it will start again. Every time.
Appliances can do many different things: Firewalls, access points, data collection, industrial control, network monitoring and so on.
It should of course be possible to update the software remotely and if the new version doesn’t fail, it should be possible to return to the old software version again.
NanoBSD is a way to build FreeBSD for use in such appliances.