The title of the play is actually a twist on a child's nursery rhyme/ Disney song.  The song "Who's Afraid of the Big, Bad Wolf?" is something that Disney copyrighted in his film, The Three Little Pigs.  The song/ nursery rhyme discusses a condition where the pigs are afraid of this larger than life figure of the "big, bad wolf" who threatens to blow down their house and conceivably destroy their world.  The wolf, in this case, represents the ultimate force of negation that comes from the outside world to the privatized world of the interior.

While writing the play, Albee was at a bar in whose bathroom, scrawled across the mirror in soap was written, "Who's afraid of Virginia Woolf."  As he was writing, the image of this question kept popping up in his mind.  He was attracted to the immediate image of the song of the "big, bad wolf."  Recognizing that it was part of the Disney empire and nearly impossible for which to gain rights, Albee settled on the idea of "Virginia Woolf" because of the homophone being able to conjure up the same image without having to go through copyright issues with the Disney empire.  At the same time, Albee thought that the inclusion of "Virginia Woolf" would add to the intellectual flair of George and Martha.  The idea is that intellectuals use concepts and a sense of the cerebral as vocabulary to hint at the emotions that lie underneath the surface.  It is for this reason that Albee writes the singing of the song itself into the drama and represents how its image is constructed back into the story.  In this, Albee found the title to work well in terms of what he wanted to convey and what it conjured into the minds of the audience.