We tend to assume that when a spouse dies, the remaining spouse will be stricken with grief. This is because we assume that most marriages are happy, and the remaining spouse loves and will miss the spouse who has died.
In this story, we can see that Mrs. Mallard's response is different because after her initial shock, when she retreats to her room, a feeling of freedom and happiness come over her. She is slowly awakening to the idea of a life without her husband, which for her implies a life without repression. She sees a blue sky, birds flying free, and hears someone singing outside her window. These are all symbols and reminders of the life she now believes she can have. She thinks of how her spouse has imposed his will upon her throughout the entire marriage, and it is first with a feeling of relief and then gradually dawning happiness that she begins to embrace this newfound freedom.
This story is often used to show the repression of women in marriages in days gone by, but I suspect such marriages still exist, and there might be any number of relieved widows out there, who can now figuratively kick up their heels and enjoy their freedom from oppressive spouses. This is not a problem that feminism has managed to solve.