An anachronism is defined as "something or someone that is not in its correct historical or chronological time, especially a thing or person that belongs to an earlier time." Belle Reve, the childhood home of Blanche and Stella, has fallen into literal disrepair and is lost to the family, but figuratively represents the idea of "The Old South" and how its antiquated ideas are no longer realistic in the current age.
In the late 1800s and early 1900s, the American South was a huge agricultural powerhouse for the United States and the world. The aristocratic and gender biased class structure instituted in the South was respected and valued throughout the world; however, the industrial boom of the 1920s made the agricultural system of the South obsolete, and with it, their societal norms.
Belle Reve symbolizes the rise and fall of this historical event. Once it is lost to the family, Blanche refuses to (or, perhaps, cannot) adjust to life without these values she's held closely for so long. She pretends to be a "Southern Belle," despite the fact that most people around her don't care or even understand what that means. Stella, on the other hand, has moved on with Stanley, a Polish immigrant who represents the new and changing ways of America. Stella, though delusional in what Stanley is capable of, is able to behave in a more socially acceptable way because she's moved on from Belle Reve, both literally and figuratively.
The conflict between Stanley and Blanche dominates the play, and with it, the conflict of the "Old South" with more current and modern times. Blanche, like Belle Reve, is unable to transition and is lost, mentally, at the end of the play.