Clinton, In a Folk Club setting, often most of the participation comes from the 'audience' or members - with guests as an occasional luxury. 'Floor singers' are singers from the audience who sing in a song circle type of way before, after or in-between the guests.
Dunno if it's English specific to this side of the Atlantic - but 'the floor' is also used in meetings - as in 'speaker from the floor'. There is therefore no connection between levels of booze consumption among your average folkie (as some might suspect).