The imaginary son of George and Martha is an illusion both of them share. They pretend they have a son so as to seem more normal by the standards of American culture, which prizes the nuclear family. Martha is infertile, so they were never able to have children of their...
The fake child is yet another example of how the play destroys the idea of the perfect little family. Though they seem like normal, respectable people, George and Martha are co-dependent, bitter, and deeply dysfunctional, resentful that their lives do not measure up to society's golden standard. They hide their abnormalities behind a facade.
Their imaginary son was their way of pretending at some kind of normalcy, but eventually, the fiction cannot hold up when Martha makes it public with their guests. This was the one "rule" of their game: the imaginary son could not be mentioned around other people. George ends up "killing" the son to destroy the illusion. The play ends with some hope that the two might be able to reconcile as a result.