With Who's Afraid of Virginia Woolf?, as well as some of his earlier plays like The Zoo Story, Edward Albee succeeded in combining two types of drama: realism and absurdism. First let's talk about realism. Realist playwrights set out to write plays that seem real: the dialogue is similar to everyday speech; the settings are everyday kinds of locations, and the conflicts are generally issues that everyday people face. Who's Afraid of Virginia Woolf? fits the bill for the most part because the characters all speak in a way that's believable, it's set in a totally normal living room, and it centers on a bickering couple.
In an Albee play, however, nothing is ever quite what it seems. What starts off as a realistic seeming situation quickly spirals into the realms of the absurd. The Theatre of the Absurd began in Europe in the wake of WWII, and was inspired by the existential philosophies of Albert Camus (who wrote many novels, including The Stranger and The Plague). In the absurdist view, there is no ultimate meaning to our lives. As a result, everything we do is therefore an absurd illusion, which we create in order to avoid the fact that nothing matters and we're all alone. Through cutting insults and gross humiliation the characters of Who's Afraid of Virginia Woolf? gradually strip away the illusions that they've hidden behind. With the destruction of the imaginary child at the play's climax, George and Martha's last illusion is destroyed. They are trapped, alone together in an absurd and uncaring universe.