Laura has more than one handicap. Besides her limp and social awkwardness, Laura's insecurity prevents her from taking on life's challenges even in small ways. She gets so nervous at tying class she throws up during class and is so humiliated that she never goes back. She wanders around town, visiting greenhouses or going to the movies until "found out"; the rest of the time she spends at home, listening to records or playing with her glass menagerie. She retreats into a crystalline world of her own; this is her means of escape.
Ironically, the fragility in Laura shatters even as her heart "breaks" when she learns why Jim will not be coming back. She gives him the unicorn without its horn, now "normal," as a souvenir of his visit. Although she is emotionally let down by this delicate encounter, she takes significant strides ahead in self-affirmation.
But even this does not arrange things for her most uncertain future. Tom later reveals that Laura is still alone, still "different." She will never be, as Amanda, the flirty woman who knows "the art of conversation." This difference does indeed isolate her but it also sets her apart as a special, even unique, person. As Amanda remarks, "Still waters run deep."
Laura is peculiar in several ways. First, she was born with a slight birth defect which made one leg longer than another. This makes her walk with a limp. Laura is very self-conscious about her leg. That, couples with the fact that her father abandoned the family and her extreme shyness makes her seem odd to other people. When Tom calls her "peculiar" he says all she does is stay home and play with her glass collection. Amanda simply refuses to acknowledge Laura's defect or her extreme shyness but she is terribly concerned about how Laura will support herself after Amanda dies. That's why Amanda nags Tom about bringing someone home to meet Laura.