The Question and Answer section for A Streetcar Named Desire is a great resource to ask questions, find answers, and discuss the novel.
The music is used to signal Blanche's memories, particularly, her husband's suicide. When the music plays, we are quickly able to correlate her past, her delusions, as well as her complete lack of reality.
At the end of the second scene, Stanley tells Blanche that Stella is having a baby?
They can't play poker at Mitch's house because his mother is sick.
MITCH [hearing this, returns quickly to the stair rail]:
No--not at my place. My mother's still sick!