Alcee, the old flame of Calixta's, walks into the story and manages to change quite a bit. Kate Chopin has a common theme of women who feel repressed and unsatisfied in their marriages. And, it's not necessarily because their husbands are cruel or even that they don't love their husbands, it is more that the "limitations" that marriage puts on women are repressing. A married woman, in Chopin's time was that and only that. They didn't have careers, many pursuits, and were not regarded as the superior gender. They were expected to behave in certain ways in their marriages and society, and were to obey certain codes of behavior when it came to sexual boundaries. Chopin's characters are often unsatisfied with all of those restrictions.
So, Alcee represents a way for Calixta to break free from those expectations, and to find "happiness" and "freedom". Through Alcee, she can fulfill her desire for excitement and diversity, she can feel desirable and appreciated, she can feel the thrill of stepping outside accepted social norms, AND she can do it all while keeping the good parts of her marriage--a loving husband and child, a house, a stable income. Alcee is the "solution" to Calixta's underlying unhappiness with her state. Chopin illustrates this as Calixta is happy instead of "overscrupulous" when the boys come home covered in mud; the last line states that, after the storm and Alcee came and all that went on, that "everyone was happy." During their tryst, Chopin uses imagery and figurative language that is very descriptive to describe the elation and bliss that Calixta experiences. She is "knowing for the first time" the joy of that experience, she
"was like a creamy lily that the sun invites to contribute its breath and perfume to the undying life of the world."
These flowery descriptions and detailed imagery relate the happiness, freedom and unleashing of joy that Alcee, in this story, represents.
I hope that those thoughts help a bit; good luck!