The color white is significant in that it is an allegory to Blanche's "clean slate". It is ironic, because Blanche had come to her sister's to possibly start over after leaving a life in shambles behind her. The color white signifies purity, cleanliness, impartiality. However, we know that Blanche represents anything but those characteristics.
Yet, Blanche enters the scene dressed impeccably in white, sending an ironic signal: I am clean. I am pure. I am innocent. And while we see her, we realize how wrongly dressed she is, as she is planted in the dirty, dusty industrial street where Stella's apartment is situated.
We, as the audience, feel how that white dress could get stained at any moment, and how embarrasing it would be for Blanche. After we read the play we realize that that's exactly what happened to Blanche: Get real self came out, and she payed for it dearly.