A room off of a primary entertaining parlour into which excitable Victorian lasses in too-tight corsets could withdraw to recover their composure and breath.
As the necessity of respiration was slowly recognized in women and the art of swooning fell into disfavour, the withdrawing room metamorphosized into a room, still adjunct to a great hall, into which cohorts might conduct business in a more private setting. Keeping in mind the previous function, and the predictably comfortable furniture for supporting persons in repose, you can imagine just what sort of "business" was often conducted. It wasn't accounting. Corsets were still loosened, if you get my drift.
In a modern era of baggy unisex clothing and sensible shoes, "drawing room" is a witty-sounding name for art supply stores. A parallel could be drawn between the withdrawing room and the chill-out room available at some dance clubs (first function) or champagne room at some strip clubs (second function).