The central problem of the story "A Jury of Her Peers" is the differentiation and subjugation of women. A woman who is subjugated to the will of men and the societal expectations suddenly seems to have snapped. In a moment of what seems to be a build-up of frustrations she killed her husband and fell into a state of shock.
As a result, she now has to face a jury of her peers to determine whether a) she is indeed guilty and b) she did it in a moment of temporary insanity. Finding out her verdict would also help establish what sort of things took place in the household which prompted her reaction.
However, she is more than likely going to lose. She is the symbol of a second class citizen (which women were then) and how the same society which imposes itself on them is now the ruler of one woman's fate.