The large and extensive glass menagerie owned by Laura Wingfield allows her to shun the real world that she neither likes nor truly understands. Furthermore, it enables her to retreat into a private world of fantasy, a place where she can feel safe and where she can exert some measure of control over her life.
Despite her mother's earnest attempts to get her to come out of her shell, Laura is simply not cut out for this world. Truth be told, she's much too delicate, fragile, and damaged to fulfill her mother's wishes and become a much-desired Southern belle. And so she remains in her comfort zone amid her large collection of little glass animals.
And yet it's not just Laura who cannot properly function in the real world. The same applies to her mother, Amanda, and her brother, Tom. As we've already seen, Amanda is unable to face up to the reality that her daughter will never be like she was in her younger days. And Tom, by retreating into a world of drink, movies, and literature, has a glass menagerie all of his own.
The eponymous glass menagerie, then, doesn't just tell us about the character of Laura but acts as a constant reminder of the chronic inability of her family to embrace reality and live in the world without illusions.