My text analysis professor taught that in order to fully understand a play you have to understand the first line, last line, and title. What play then is a better candidate for this exercise than Who's Afraid of Virginia Woolf? The title doesn't really have a whole lot to do with the dramatic arc of the play other than the fact that it shows up a couple of times and with some dramatic irony at the end. (GEORGE: [sung] Who's Afraid of Virginia Woolf. MARTHA: I am George.)
Well, the parody song is not only vastly important, it's the key to the play.
Martha and George have build their marriage on a sand foundation. There were all the expectations for George in the supposed succession in the college. The welcome parties that they are expected to host and all the games they have to put their guests through. And most of all, their son and all the deception and baggage associated with that. Through out the course of the play, the two characters proceed to slash through all the lies and deception until there is nothing left. Nothing left, that is, except to be afraid of Virginia Woolf.
That fear of being fully exposed, standing naked in front of the other person is where we end the play. They are left with nothing but each other. In the end, isn't that what we are faced with? There are always defense mechanisms and evasions that keep us insulated from each other, from being hurt, and from fully opening up. George and Martha trod a violent and destructive path to catharsis, but there is some hope in the ending that they've finally broken through and their lives can change. Whether this fixes their relationship or not, we are never told. But something has to change and their relationship will never be the same again.