This is a very good question, and I have included a link below to the historical context in which Chopin wrote this excellent novel to give you more information. Of course, it is very hard for us in our context to appreciate such a radically different historical context, but it is important to remember that women led very different lives back in Creole society in the nineteenth century. Women were dominated by men and were expected to do nothing more than look after the home and bear children for their men.
Now, consider Edna's presentation of the novel and the way that she is given the dubious privilege of voicing the concerns, desires and passions of women, who often had to subdue them or keep them suppressed. Edna represents a bold female character who, in her infidelity and desire for a life where she can have a voice, goes entirely against the society and culture of the time, deliberately rejecting the expected roles of society in terms of being a wife and a mother. The description of her sexual awakening and also the way that she commits suicide all served to make this book a scandal at the time of publication.
This is a good question, and to understand it, you need a historical lesson, too. Chopin wrote her sexually charged novel (hence the title) in 1899, on the cusp of repressive Victorianism. In fact, it was so controversial that the literary community largely ignored its publication; it was her second, and last novel.
Part of the scandal is content. Edna Pontillier, a wife and mother, commits every 'sin' of the age. She has an affair, she dresses indecently, she lives on her own, fights convention and finally commits suicide (sorry for the spoiler if you haven't read it). It's widely regarded as a piece of feminisit literature, well before its time. But, I think a major part of its controversy is that Edna eschewed her duties as conventional wife and mother, choosing instead to live life on her own terms and disregard societal expectations. A secondary explanation is Edna's experience of a physical and sexual awakening, a scandalous disclosure in the late 1800's. Finally, her suicide. Back then, religion played a major part in societal expectations, and suicide would have been regarded as a major taboo.
Hope that helps.