Tom is trapped by his responsibility for supporting his mother and sister. He has dreams of being a writer and of travelling. Neither can be accomplished while he is trapped by his job in the shoe warehouse. His escape is initially to alcohol and the movies, but he ultimately joins the Merchant Marines and abandons his family.
Laura is trapped by her disability and lack of self-confidence. She is unable to function in a larger society, whether that is in high school or business school. She can't bear what she feels as the scrutiny of others. She escapes into the world of her glass menagerie, revelling in their beauty and fragility.
Amanda is trapped by her disappointment in her children. Neither are able to achieve what she had hoped for them. She escapes into her memories of her Southern belle past.