In answering the inherent question in the thread title, I would say a UK Folk club it is a place where people with similar interests can get together and socialise while sharing their common enthusiasm for a type of music that reaches their very essence. My personal feeling is that the key element is the socialisation. Virtually all my current circle of friends I have met through my folk activities.
When my first marriage broke up it was the folk world that held me together and which helped me create the life I now enjoy, and boy do I enjoy it! I've seen the same healing and supportive aid being administered to other people in need.

As to the nature of clubs, I agree with most of what has gone before. My preference is definitely not 'concert clubs' although I will go to them if there is an artist or act that I particularly wish to see. They are inherently unfriendly compared to the more common general format clubs and tend to have set group of 'residents' so you don't get the variety of performance that the 'general clubs give you. To be honest there are some concert clubs where you feel that the residents/organisers run the club to give themselves a weekly ego trip.

I have been fortunate in the clubs I have been able to get involved with, the singaround clubs in Bedford, Readifolk in Reading, Uxbridge, Maidenhead and Herga in NW London are all 'singer based' clubs, promoting floor singers as well as providing 'professional' guests.
The culture of the clubs I like is that everyone is accepted no matter how good or bad, experienced or raw beginners they may be. Obviously we all prefer to hear good performers but the folk world's acceptance of anyone who is willing to offer a contribution is what makes it special. The song is the thing, not the singer and not the level of performance.

I have no experience of the American folk scene but as I understand it from friends that do, the Americans expect for more talk and introduction to the performance of a song than would be expected or appreciated by a British audience. The song's the thing, unless the talk is a key part of the performer's act.   

Enough hovering.