So Im no english major or anything, but I do love this story. Ive discussed and read many discussions on this short story and to my best knowledge this is what it meant:
There are several passages that represent supernatural themes, talking about the descriptions of the mother (hands, buck teeth, in the eyes of a child could be claws and fangs), the dress compells the child to defend her mother's memory. Also, the grandmother's line 'Oh god its happening again' (not an exact quote, Im sure) makes it sound as if it is a curse, or something along those lines that is inheritaded by the daughter.
My take on it, regardless of the supernatural undertones, is that it is a story about how we can inherate our parents mistakes, genes, etc, or in this case monsterous tendancies. I see it as a coming of age story and how this child either A) lost it completely and killed her friend because of the negative things she said about her mother OR B) the situation, between the stress of hearing horrible things about her mother who could do no wrong in her eyes, and perhaps puberty, and definetly putting on the dress brought about a change in the daughter. I would think her mother was a vampire, witch, werewolf or something along those lines and the dress is somehow connected to all of it. This is most likely why the grandmother tried to keep it locked up and away from the child.
Anyway, I may be completely off base, but this is what I took from it. :)