The storm is a super obvious symbol. It's involved in practically every element of the story. First off, it's the title. Second, it plays a huge role in the plot, forming the beginning and the end of the story. It also plays a really important part in the middle by bringing Calixta and Alcée together, pushing them into each other's arms and giving them the time and space to get physical before the world outside returns to normal.
From a literal standpoint, the storm is a frightening occurrence in the natural world. Alcée describes it as "a cyclone" (2.13), while Bobinôt can tell right away that it's "sombre," "sinister," and "threatening" (1.1). Chopin describes the rain pouring down with a repetition and regularity that suggests rain itself. Let's check out how the storm builds:
Of course, it's when all that rain is coming down most passionately and ferociously that Calixta and Alcée are exploring their feelings for one another to the fullest.
Many critics have observed that the storm's passion is similar to that shared by Calixta and Alcée. As scholar Joanna Bartee points out, for example, "Chopin uses the image of the storm to represent the sexual tension that builds throughout the story between Alcee and Calixta" (source). You could say, for example, that the lightning and thunder playing outside Calixta's home foreshadows the sexual encounter that is about to take place:
A bolt struck a tall chinaberry tree at the edge of the field. It filled all visible space with a blinding glare and the crash seemed to invade the very boards they stood upon. (2.14)
Compare that to the way Calixta and Alcée's bodies come together, as described just a few paragraphs later:
When he touched her breasts they gave themselves up in quivering ecstasy, inviting his lips. Her mouth was a fountain of delight. And when he possessed her, they seemed to swoon together at the very borderland of life's mystery. (2.21)
The lightning bolt is described more clearly than the "possess[ion]" that follows, but they both get at the same thing: a huge, albeit temporary, explosion of energy and feeling.
If you'd like to read more about the storm, check out one of these sections: