Blanche's first words in the play describe the route she is supposed to take to Stella's home:
They told me to take a streetcar named Desire, and then transfer to one called Cemeteries and ride six blocks and get off at—Elysian Fields!
Williams's stage directions refer to the "slightly hysterical humor" with which she says these words. Blanche's temperament and education, as well as her position as an outsider, make her alive to the poetic allusiveness of the words which, to locals with other things on their minds, seem nothing more than a mundane sequence of directions. Blanche thinks about the name of the streetcar and immediately recalls it when Stella is talking about her physical attraction to Stanley:
What you are talking about is brutal desire—just—Desire!—the name of that rattle-trap streetcar that bangs through the Quarter, up one old narrow street and down another.
Stella immediately asks if Blanche has ever ridden that streetcar, a question Blanche chooses to take literally but which is clearly intended as an enquiry into Blanche's own desires. The name of the streetcar thus comes to stand for all the desires, frustrated and satisfied, that drive the narrative of the play. When Mitch is about to escape at the end of an unsatisfactory date, Blanche wonders whether he will be using the streetcar named Desire to get away from her.
As a symbol, the streetcar also stands for the relentless, mechanized world of the city, Stanley's world, which is opposed to the "beautiful dream" of gracious living symbolized by Blanche's Belle Reve. The dream, like the great house, is static and lost, whereas desire, like the streetcar, drives one relentlessly onward.