There are a number of different ways that this question can be approached. I suppose the most obvious one would be to analyse this play as a comment on the roles of women in the society of the time of writing, especially how women's roles in the South were even more narrow and constrained than elsewhere. This of course is shown most stridently in the figure of Blanche, who, although she is clearly educated and intelligent, is shown to be hampered by the gender roles in Southern society. These restrictions dictate that women need protecting by men, and also do not allow her to be sexually licencious in her behaviour. What draws this behaviour into attention is when Mitch discovers her past exploits and rejects her as a result, highlighting the gap between the reality of how women really behaved and the public fiction that they were expected to maintain.
Williams himself wrote of this play that this was a kind of pageant to the South and the cultural values that were fast disintegrating. If we take Blanche as a symbol of these values and their inconsistencies and how they are unable to meet reality, we could argue that the play therefore is really about the destruction of an antiquated set of values that are anachronistic in modern society. Just as Blanche is taken away at the end, so the set of moral codes and values are consigned to the historical garbage bin as they are replaced by newer and in some ways more brutal values.