Albee wrote Who's Afraid of Virginia Woolf? while America was in the midst of the Cold War with the U.S.S.R. The two nations had teamed up against the Nazis in WWII, but it didn't take long for them to turn against each other after they no longer had a common enemy.
America's commitment to democracy and capitalism was the ideological opposite of the Soviets' communism. While American's valued individual liberty, the Soviets thought individuals should be more concerned about what was good for the whole. (It's a lot more complicated than that. For details check out Shmoop's entry on "Cold War: Causes & Origins."
The specter of the Cold War looms large in Who's Afraid of Virginia Woolf? The vicious verbal battles between the characters, could be seen a symbolic of the war as whole. This is perhaps most clearly shown when George and Nick are fighting about genetics. In this battle George seems to come to represent American Democracy while Nick represents Soviet Communism. George complains that with the rise of genetics "There will be…a certain loss of liberty […] diversity will no longer be a goal […] ants will take over the world" (1.596). This sounds an awful lot like what an American might say of Communism. Another big clue here is that George references ants. The cooperative social structure of an ant colony is a model for a communist society.
George and Nick's names are also symbolic of American/Soviet tensions. George is named after George Washington, making him symbolic of America. Nick could be named after Nikita Khrushchev, the Soviet leader, so he could represent the U.S.S.R. Also, George tops off his lecture of the horrors of genetics by saying, "I will not give up Berlin!" (1.600). This is a direct reference to cold war tension. The German capitol was divided in half – one side U.S. influenced, the other under Soviet control. The divided city was a symbol of the ideological divisions of the world. By using the word Berlin, Albee weaves all these shades of meaning into the scene.