Edward Albee's Tony Award winning play Who's Afraid of Virginia Woolf analyzes many different aspects of "the American family" during the mid 20th Century. Society's 'picture-perfect' family during these times was the image of a happily married husband and wife with beautiful children. Think about famous television shows from the 1950s. Sitcom families were portrayed as a working husband and a loving housewife with children.
Martha and George are symbols of the opposition of that, representing all of the 'normal' families in America who did not live up to these sometimes unrealistic societal standards. Martha and George are still together, but they obviously fight with each other and get some dark satisfaction from insulting one another. They do not have any children due to Martha's infertility. George has a job at a University, but is not at a satisfactory position level. Martha is not a loving housewife. One could argue the combination of all these things have made Martha and George feel slightly embarrassed, guilty or resentful that their 'picture-perfect' family does not exist. Their controversial decision to imagine a child is a product of this. The illusion of a child is a distraction for George and Martha from the unhappiness of their life together. The only real bond they have forged is over an illusion. That illusion is destroyed by George, who "kills" off their son.