Blanche and Mitch have just concluded their date at an amusement park. It didn't go well. Blanche tried hard to be happy, but could not "rise to the occasion." At the doorway to the apartment, he asks to kiss her. The audience learns through their conversation that this is not their first romantic interlude. There have been other dates, and Blanche has been allowing him to kiss her, but go no further physically.
Mitch reveals his emotions with this heartfelt line:
MITCH: I like you exactly the way that you are, because in all my - experience - I have never known anyone like you.
And then Blanche laughs at him. Keep in mind, that Blanche has been dating Mitch in hopes that he might be a potential husband, or at least someone to provide her a sense of security. The fact that she laughs at him when he is trying to make their relationship more serious shows that part of her (perhaps the mentally unstable part) is bent on self-destruction.
When Mitch realizes that his romantic and sexual advances are thwarted, they begin to talk about Stella and Stanley. Blanche speculates upon Stanley's hatred towards her, wondering if there is something else behind the hostility - perhaps lust.
Mitch bluntly asks to know Blanche's age, claiming that his ailing mother wants to know. Blanche changes the subject and proceeds with a long monologue about her tragic past involving her deceased husband. She and her young husband, Allan Grey, became engaged at a very young age. Shortly after the marriage, she walked in on her husband having a sexual encounter with an older man. Later that evening, while on the dance floor, she whispered to her husband, "I saw! I know! You disgust me." Her husband responded by leaving the dance floor and shooting himself.
After telling her story of her regretful younger days, Mitch seems even more interested in taking their relationship further. Blanche ends the scene with "grateful sobs."
BLANCHE: Sometimes - there's God - so suddenly!