Age
Grandma is the character who represents the elderly in America, a group that has become marginalized and pushed aside, especially according to her. Grandma is often ignored by Mommy and Daddy and silenced whenever she wants to say something, even if she has a salient point. The general impression is that Grandma has nothing worthwhile to say, and she is dismissed for her age. Her ideas and words are seen as being obscene and uncontrollable, and both Mommy and Daddy call her out for making sounds that are considered inappropriate in formal social contexts. Meanwhile, Grandma maintains that she is silenced because of her age, and that this is what kills old people. At one point she says, "Most people think that when you get so old, you either freeze to death, or you burn up. But you don't. When you get so old, all that happens is that people talk to you that way." She is referring to the fact that age has less to do with the actual old person and more to do with how society and people treat the old person.
The American Dream
As the title suggests, the play examines the concept of "the American Dream." The play mocks the idea of the perfect American family and the notion of the American dream. In showing the ways that reality does not align with the illusions and lies that the characters hold, Albee shows the ways that the American Dream is an elusive fantasy. When the Young Man shows up, Grandma immediately identifies him as "the American Dream," but he soon reveals himself to be empty, incomplete, and incapable of love. He is an absurd and implausible character, and Albee directly signifies him as representing "the American dream."
The play examines the ways that Mommy and Daddy are chasing happiness and a certain version of the American Dream—financial stability, the perfect nuclear family, social status—and the ways that their pursuit has made their lives all the harder. Their drive to present the image of prosperity and happiness makes them behave horribly towards one another and to treat others poorly, as most starkly evidenced in the story about their adopted child that they brutalized.
Disfigurement
Another major theme in the play is disfigurement. Grandma becomes disfigured with age. At one point she says, "Nobody hears old people complain because people think that's all old people do. And that's because old people are gnarled and sagged and twisted into the shape of a complaint." In Albee's world, the shape of one's body reflects a deeper truth about a person.
Additionally, Mommy and Daddy disfigure their first son when he refuses to listen to them and become what they want him to be. Ironically enough, because the baby does not fit into standard norms of society, they alienate it more by disfiguring it and committing violence against it. Thus, the characters disfigure themselves or those over who they have power because they wish to be accepted into the world or they wish to make someone else adapt to socially-accepted norms.
Emasculation
Compared to Mommy, Daddy is quite docile and submissive. He is often intimidated and pushed around by the more willful Mommy. It seems that he would rather just keep the peace and the status quo rather than ruffle any feathers. Mommy's domination of Daddy highlights the ways in which their relationship is built on her emasculating him. This dynamic comes to a head when Mrs. Barker rings the doorbell and the married couple debate about whether to open the door. At one point, Mommy references a moment in which Daddy was "firm...masculine and decisive." Daddy can hardly believe it, asking, "Was I really masculine?" When he still doesn't answer the door, Mommy emasculates him, saying, "Oh, look at you! You're turning into jelly; you're indecisive; you're a woman." She goes from telling him he's masculine to calling him a woman, as though it were an insult. This is enough to spur Daddy to open the door. In this moment, we see explicated the dynamic of emasculation and humiliation between Mommy and Daddy.
Family
Family is one of the most prominent themes in the play. After all, the two central characters are simply called "Mommy" and "Daddy" and they are helping to take care of Grandma in their apartment as she ages. Mommy and Daddy are, in some ways, specific characters, but in other ways, they are archetypes of maternal and paternal figures in America. Mommy is domineering and strong-willed, while Daddy is weak-willed and supplicant. Grandma is the archetypal grandmother, salty and snappy, making wisecracks, but never respected as much as she ought to be. Having established these archetypes, Albee dismantles the concept of the traditional American family by obliquely uncovering its buried and shameful secret: an adopted son whom Mommy and Daddy disfigured.
At the end, the promise of a family is restored by the arrival of the Young Man. While Mommy and Daddy don't know it, the Young Man is the twin brother of the baby whom they killed. They are haunted by the image of a perfect family that they could not achieve.
Confusion & Vagueness
The play is absurdist and not realistic in any way. One way that this manifests in the text of the play itself is in the fact that the characters are often confused about the nature of reality, and reality itself is a very slippery set of facts. While everyone maintains that Grandma is the least tuned in to reality, made senile by age, she is often the most reliable index to the truth, especially in comparison to those around her. At the start of the play, Mommy and Daddy are waiting for the arrival of someone, but it is unclear who exactly. It seems like it could either be some kind of landlord for their apartment or the "van men," who are meant to take Grandma away. When Mrs. Barker shows up, they do not know who she is, and neither does she. At one point she purports to be the chair of the woman's board, but it is curious that Mommy doesn't recognize her if that's the case.
The confusion and vagueness only continues when Grandma tells the story of the adopted child. While we can surmise from Grandma's telling that the adopted child belonged to Mommy and Daddy, she never says so; rather, she describes everything in the story as being "much like" an element of reality. Slowly, we begin to realize that the story she is telling is not about other people at all, but about Mommy, Daddy, and Mrs. Barker. The lines between reality and story are blurred, and no one can quite tell what is the truth.
Social Status
Mommy is a very high strung personality who seems particularly preoccupied with achieving social status. The part of the play that illustrates this most vividly is when she relates the story of buying the beige hat. She tells Daddy that she left the store thinking that her hat was beige, but when she encountered the chair of the woman's club (a woman with a higher social status than herself), the chair remarked that the hat was wheat-colored. In spite of the fact that she liked the hat as it was, Mommy returned to the store and made a scene, demanding that they bring her a different hat. The employees of the store go into the back room and bring her back the same hat, which she knows, but she doesn't mind. It was just enough for her to have thrown a tantrum and established her superiority over the store clerk. Thus we see that when Mommy feels like she's been made to feel inferior (as she did with the chairman of the woman's club), she takes it out on other people, whether it's logical or not. Social status and saving face in the eyes of society are both very important values to Mommy.