The title of Tennessee Williams's play A Streetcar Named Desire is taken from a quote spoken at the beginning of the play where Blanche says the following words to a woman on the street in Scene One.
They told me to take a street-car named Desire, and transfer to one called Cemeteries, and ride six blocks and get off at—Elysian Fields!
The entire quote is metaphorical and offers foreshadowing on Blanche Dubois's life, and how it will become, now that she is in New Orleans visiting her sister Stella and Stanley, Stella's rude and abusive husband.
For example, "desire" is the basic driving force in the play. Blanche's own desires for money, position, sex, love, youth, attention, and much more is precisely what drags her to the bottom of her misery. Stella's marriage is based on sexual desire and control. She, too, build her own misery by marrying Stanley, who seem to satisfy her desires while abusing her psychologically and physically. Stanley's desire for power is what makes him treat women like second class citizen, and what ultimately leads him to rape and basically destroy Blanche's life.
The words "Elyssian Fields" are significant in meaning because they serve as an alternate symbol for the word "Asylum", which is where Blanche will end her days, and because the Elyssian fields are synonymous with the mythological Land of the Dead. That is also the name of the street where Stella lives.
Although Blanche does not die, she does experience a similarly sad demise: Her life as she knows it, ends in shame. She loses her big Southern mansion when her father dies, she loses her position in society when the money runs out, and she loses her reputation and dignity when she resorts to escorting men out of a hotel room. She even loses her chance at teaching when she has an affair with one of her students. Hence, Blanche does experience a kind of death: She is now a broken woman.
Hence, the importance of the title is that it shows that desire is the force what will "drive" the action of the play, and the mechanism that will end up destroying or changing the lives of each of the main characters.