The theme of appearance vs. reality in Streetcar Named Desire is most obviously seen in the character of Blanche.
Blanche tries to give off the appearance and maintain a reputation of being genteel, proper, reserved, educated, and sophisticated. She tries to appear as a person from the Old South.
In reality, she sneaks drinks every chance she gets, tries to seduce a boy when she finds herself alone with him, flirts with Stanley, and has a secret past that finally gets revealed.
This is not to say that Blanche is not at all sympathetic. She is, at least in some ways, in a no-win situation. The economy in the South was destroyed by the Civil War, and numerous plantation owners (as Blanche's family was) never recovered. As she says in the final scene, she has always had to depend on the kindness of strangers--specifically, men.
Perhaps the most moving example of appearance not meshing with reality is the reversal in the final scene. Blanche actually tells the truth about being raped by Stanley, while Stanley lies. Blanche's means of coping is to hold on to the hope that her old friend is coming to rescue her, a hope everyone, both the other characters and the audience, knows is false.