A BNC connector is used with co-axial cables. One part of the connector is male and is the part that is usually stationary on a piece of equipment, while the other part, as shown in photo,  is the female part that twists, and locks onto the male part.
What does BNC stand for? Well I asked around and got a few different answers, I read a letter to the editor of VideoMaker Magazine that asked the same question. I responded with this letter:
"The article in Quick Focus (May ‘95) about the acronym BNC, and what it stood for, was well timed with a course I just took.
The instructor in our Networking class asked the students if anyone knew what BNC stood for. Having researched this at one time in my life because we use these connectors quite heavily in electronics/computers, I replied quickly, and authoritatively: “British Nut Company”. After the laughter stopped, the instructor said no, that BNC stood for “Bayone-Neil-Concelman”. Since I hadn’t yet lived down my humiliation, I didn’t catch the story that followed about the origins of this name. Supposedly it had something to do with the guys who invented Ethernet.
Note the name “Neil”, above, whose name is also in one of your (VideoMaker Mag) definitions, Bayonet Neil Cofflin.
I did further research after this and to say no one is really sure of WHAT the letters stand for, would be an understatement.
Barrel Nut Connector  (makes sense!)
Bayonet Neill Concelman-  Blackbox, Zendex
Baby N Connector- EE Circuits archive
Bayonet Neil Concilman - Analog Devices 
British Nut Company
Bayonet Nut Connector 
Bayonet Nut Coupling - King's Electronics (manufacturers of BNC)
British Navy Connector - ATT
Bayonet Neill Concelman - Electronics Now
Thanks to the internet and numerous "acronym sites", I found a few more, some just a difference in spelling of the supposed inventors, Neill and Concelman.
British Naval Connector 
Bayonet Nut Coupling 
Bayonet-coupling Navy Connector 
Bayonet-coupling Nut Connector 
Bayonet Navy Connector
Bayonet Neil Councilman 
Bayonet Nipple Connector 
Bayonet Norm Connector 
Bayonet Normalized Connector 
Bayonet Nut Coupler 
Big Nobby Connector - I like this one...
I suggest the most definitive answer (the one I believe) is that the connector was named after the Bayonet (push and twist) locking mechanism and its two inventors "Neill" and "Concelman".
BTW (by the way), RHF stands for Robert Henry Found....though there could be other interpretations...