One of my favourite films ever is "Who's Afraid Of Virginia Woolf", based on a successful stage play. If you haven't seen it I would recommend it. Absolute tour de force in mind games and visciousness from Elizabeth Taylor and Richard Burton. Both on top form getting one over on each other whilst entertaining a naive young George Segal and Sandy Dennis.
I believe its a play on words. Comes from "who's afraid of the big bad wolf?" which Taylor's character was consumed by. I don't know any more than that though.