Hi George
No doubt you're familiar with the Mac Mini... small footprint; low power usage in standby [particularly for 24/7 usage]; modest to impressive performance depending on the specs chosen at purchase.
These can be used as Desktops in Home and Businesses... but they can also be used as "Entertainment Centres" under a TV at home, particularly as a HTPC or Video Server.
Well the Intel NUC's and the units based on them, are just Windows versions of the Mac Mini... small(er) footprint; low power etc., etc.
The NUC's are typically listed on Amazon et al without Hard Drives and Operating systems, and sometimes without graphic cards... allowing the user to configure the computer to suit their requirements.
However, by the time a NUC is configured with a Drive and OS, the cost difference between the NUC and Mac Mini will typically be pretty small.
NUC's are very handy devices for the more "enthusiastic" and knowledgeable out there... but as they don't necessarily come ready "out of the box", I'm not sure they are the most appropriate devices for everyone.