Expressionism is a style of literature based on a narrative that explores the psychology and emotional foundation of the narrator, rather than the telling of facts. It is similar to a stream of consciousness in that emotions and opinions are stronger than facts and details, but the narrative is not as different in style as it is with stream of consciousness.
The Glass Menagerie is an expressionist piece of literature because it depicts a specific situation using Tom's own emotions and opinions of it. We see in the end of the play how Tom compares his mother and his sister basically to a shadow play that will never cease to change. He characterizes Amanda and Laura, as well as Jim, as parts of the story of his life. It is through Tom's strong views and emotion that we can create an opinion of the rest of the characters. This is basically what makes The Glass Menagerie an example of expressionism.