The title comes from rewriting the words to the children's song, "Who's afraid of the big bad wolf?" It comes up as a joke at Martha's father's party. The song is significant because it ties together the themes of childhood and parenthood, reality versus fantasy, and career success. The couples in this play do not have any children and remain tied to their parents. Martha and George rely on Martha's father for his position and his paycheck. Honey and Nick rely upon Honey's father for the money that he left them. This song, bastardized from a children's ditty, shows how all four characters in the play still function more as children than they do as adults. The fact that the name is changed to "Virginia Woolf" is also significant. In her writing, Virginia Woolf attempted to reveal the truth of human experience, emotion, and thought: all of the things that the couples in this play try to cover up. When the couples sing the song together, then, they are making fun of their own fear of the truth. George, who seems to want to get back to some truthful interaction with Martha, only sings the song when he tries to overpower Martha's disparagement of him, when Martha is necking with Nick, and when he tries to comfort Martha in the end. If one looks closely at these three different moments, it is clear that George uses the song to stop Martha from revealing truth about himself, to tease Martha for hiding from the truth behind an affair, and to give her courage to live without the phoniness they are used to. The song is consistently tied to moments in which the characters are projecting, or attempting to project, a false image. Finally, the song also ties into the theme of academic competition at the unnamed college where George and Nick work. Virginia Woolf is known to be a complex, difficult writer. Because she is an intellectual challenge, no one competing to demonstrate intellectual power would want to admit to being afraid of not understanding her writing. The song is a witty joke, but it also represents the very real, though also very petty, fear so common in intellectual circles.(sparknotes)
