Chopin uses the storm as a foreshadowing of the coming stormy affair between Alcee and Calixta, and also, a symbol of Calixta's underlying unhappiness in her marriage.  There is not much else to indicate that Calixta is unhappy or unsettled about her life.  We get only descriptions of her sewing, but as she sewed, she "felt no uneasiness for their safety," referring to her husband and son.  She is just busily sewing, without much thought in her head, so there is no indication that she is on the cusp of committing an affair with an old flame.  Chopin has her declare of the rain, "My! what a rain! It's good two years sence it rain' like that," possibly symbolizing that it has been quite some time since she has felt passion or happiness in her life either.  So, it is a symbol of her emotional state. So, the storm symoblizes her underlying unrest, and foreshadows the change that is about to occur.

Along with being a symbol of Calixta's unhappiness in marriage, and foreshadowing of the coming affiar, the storm also is a necessary element of the action, or the plot. Without the storm, Alcee would not have needed to seek shelter in Calixta's house.  That event was necessary in order for the affair to occur.  So, it is also just an elemental action or bit of plot that is necessary for the events of the story to occur as they do.

Chopin often uses the weather to symbolize events or feelings in her stories.  In this story, the storm is the unrest and coming changes that occur.  In another story of hers, "The Story of an Hour," Chopin uses a sunny sky and perfectly green leaves and good weather to symbolize the main character's happiness after her husband dies and she realizes that she is free.  So, when reading Chopin, keep in mind that she uses the setting and the weather to model her main character's inner feelings quite often.  I hope that those thoughts help; good luck!

In "The Storm" how does Chopin use the storm as a symbol? In other words, what does it represent?

In Kate Chopin's "The Storm," the "tempest" functions in several capacities.

First and foremost is the literal occurrence of the storm. It is what keeps Bobinôt and his son, Bibi, from returning home. It is also that which leads Calixta outside to take in the laundry, running into Alcée, (her lover from Chopin's previous story, “At the ’Cadian Ball”), who is looking for shelter from the weather. (Since the affair, Clarisse has married Alcée and they have children as well.)

The storm is the catalyst for the events of the story: had the weather been clear, the lovers would not have been forced together, and thereby given the opportunity to pick up where they left off.

Symbolically, however, the storm refers to the passion between the two lovers as they make love. It can also, however, refer to the angst they feel in their "restrictive" marriages where frustration, boredom, responsibility, and desire all explode with the violence of a thunder and lightning storm.

The calm after the storm refers to the improved state-of-mind for Calixta, who because of this physical release is joyful when her family returns; for Alcée, who writes to his wife that evening (she is away) to tell her he misses her, and to generously tell her that she can stay longer if she wishes (with no evidence that he has plans to see Calixta again); and, Clarisse, who is also finding marriage restrictive, welcomes the opportunity to enjoy her freedom a little longer.

The lovers, from Chopin's view, have had some "innocent adultery," (something I disagree with—but which is typical of Chopin's themes); this allows them now to return to their lives happier people, seeing to the greater good of all—as Chopin sees it.