There's that poem by Billy Collins about finding out what a poem means. He says his students just want to beat a confession out of the poems to find out what they mean, and in a way, there is a little bit of that dilemma facing the analyst of this play, because the play is organized like a poem. The characters are clearly depictions of natural forces, and they are in dilemmas that seem essential and absurd. Perhaps the best course of action would be to say that the play doesn't "mean" so much as it points to the absurdness of meaning.
For example, contrast the characters that Billy loves. There is Bananas, a woman driven crazy by the claustrophobic role that women are placed in through marriage, and there is Billy's discontent with her—a clear irony, because he feels she is the noose around his neck, and she clearly feels the same way about them. They are trapped in a loveless marriage, but when Bunny shows up (whose name is Flingus, which should not inspire hope), Billy's selfish desperation is shown to succeed. Bananas dies and he gets to run off with his mistress, but to say Billy wins is a misreading of the play. Instead, the reader should consider that Bananas is the ultimate depiction of what happens to women who love Billy.
Billy is an engine for taking healthy people and making them crazy. How does he do this? By ingratiating himself into other people's emotional lives. He tries to do this in the opening scene where we meet his character. He takes a passive aggressive stance with the venue because they don't stop and listen to his music. He is completely unhappy unless he is the absolute center of attention. He wants to receive praise and attention, but ultimately, the praise he wants is uncalled for. The absurdism of the play is that it suggests that Billy just wants to be a god. He wants to get what he wants, no matter how selfish his desires, no matter who gets hurt in the process, and then he wants praise and attention from everyone.
