"The Glass Menagerie" is the perfect title for the play as Laura's collection of glass animals is a major symbol in the play. Tennessee Williams used a LOT of symbols in the play (the victrola, the dad's portrait, the ballroom outside, etc.), but this collection underlies one of his major themes. In many of his plays, Williams is interested in what happens to society's outcasts. Certainly, Laura is one of those outcasts. Because of her handicap, she developed into an extremely shy young woman. A very fragile young woman. Just like her glass animals, in whom she finds comfort and escape.
One of the most poignant moments in the play comes when she talks to Jim about the unicorn, her favorite piece. He asks about them being "extinct in the modern world." He may have been talking about Laura - her type does not have a place in the modern world either. After they dance a bit, the table is bumped and the unicorn loses its horn. Laura assures Jim that it is all right, that now the unicorn may feel less "freakish" and will be able to play with the other horses. The hope may have been that Jim was able to get Laura to also be less "freakish" and connect with someone outside of the immediate family. Unfortunately, that hope is dashed when it is discovered that Jim as a fiance.