Jung's archetypal criticism attempts to discover the basic existentialist, metaphysical, and psychological philosophies proposed by Karl Jung, as they appear in literature.
To illustrate an example, there are certain cliches that tend to occur in literature, for example, the femme fatale, the martyr, the Cinderella-type, etc. In Jung's opinion, these archetypes tend to repeat themselves in literature as part of our deep, human connection which is sometimes even metaphysical. This is what Jung deems as the "collective unconscious."
In The Glass Menagerie we see Tom as the martyr, somewhat, since he had to overcome his mother, his sister, his situation, and himself, in order to escape the pressure of everyday life with Amanda.
Laura represents the hidden ego, too scared to come out, and terrified of the world. She is suppression itself, combined with immaturity and lack of support. She is the incomplete self.
Jim is the destitute hero whose former glory was replaced with the sad reality of a society that is nearly bankrupt. He accepts his life and moves on the best way he knows how- by accepting reality and continuing his journey in peace. Contrastingly, Tom is the one whose pathos is too overbearing to handle. Hence, Tom is a stronger Jungian archetype than Jim.
Amanda is more of a femme fatale (or used to be back in her day) and still uses her charms, perhaps in cathartic allusion to what she wishes for her daughter to do.
In all, each character is representative of a different unfinished business, and a different type of incomplete journey. This is true to most individuals, and it is a repetitive theme across literature. This connection between human emotion and the collective unconscious is what gives the theme to the Jungian criticism.