In my opinion, this story portrays marriage as an institution that is harmful to women. It is saying that women who are married tend to lose their personalities and their ability to have a life separate from their husbands.
We can see this in the way that Louise Mallard reacts to the "death" of her husband. When she believes that he is dead, she comes to realize that now she is "free." She sees that there will come a series of years that "would belong to her absolutely." During these years, she would be able to "live for herself."
If this is what she is thinking when she thinks her husband is dead, it implies that her married life is the opposite of all these things.
First, I think it doesn't say anything about "marriage," but does say something about the role of marriage in some women's lives at a particular moment in time (lots of words :)).
If you think of "Hedda Gabler" or "The Doll's House" you get pretty much the same idea/experience. Women were often seen as men's "servants" rather than as their partners; thiir choices in life were very limited, and it's clear that they felt stifled. The joy that Mrs. Mallard experiences is not so much about her husband's supposed death, as it is about the new freedom she expects for the rest of her life.
I don't know if this feeling was common to all marriages of the time, but it clearly the case in this story and the plays I mentioned.