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.
the storm represents her passion with Alcee, her former lover. although both Calixta and Alcee have families their desire for each other was satisfied.