To add to what the previous respondent has stated, this scene is clearly the climax of the play, but Blanche's sanity has been in question long before this. This is the final straw that finalizes her break from reality that began when her husband killed himself. His suicide was a reaction to Blanche's discovery of his homosexuality, but it also led Blanche on a path of self-doubt. She feels that the only way she can give herself worth is to be attractive to men, and she leads them on in order to bask in the glow of their affections. This does not work with Stanley. He sees through her and takes what he wants to take from her, leaving her shattered when the only illusion that she had to keep her going, her beauty and desirability, is thrust in her face.
The climax of A Streetcar Named Desire is when Stanley Kowalski rapes Blanche Dubois the night when they are left alone in the house. You can see the build up to this moment on that same scene, when Kowalski begins to mentally torture Blanche reminding her of her past in Laurel. He also tortures her by throwing in her face the fact that she will not be receiving the supposed gentleman caller who is rich and will take her on a vacation. Right when she is at the bottom of her humiliation, he throws the last blow by raping her. This experience made her lose her sanity. She ended up being taken to a mental institution.