You might find it useful to examine Amanda's speech in this crucial scene when she is confronting Laura about her deception and asks her what kind of life they will have in the future if she doesn't train herself up to get some kind of employment. Amanda paints a bleak picture of what future they can expect, but in her speech she signals two symbols:
So what are we going to do the rest of our lives? Stay home and watch the parades go by? Amuse ourselves with the glass menagerie, darling? Eternally play those worn-out phonograph records your father left as a painful reminder of him?
Note how the phonograph records are shown to be a symbol of Laura's father, and we can see how important they are to Laura (and, by implication, the memory of her father itself) by how she repeatedly plays them. Likewise, the glass menagerie becomes a powerful symbol of Laura's fragility and isolation. Of course, this symbol is developed more fully later on in the play when Laura talks to Jim about the menagerie's importance to her.