The story is conveniently divided into five sections that pretty much correspond to the classic plot analysis categories. Section one is just a description of Madame Aubain's house and Félicité's work as a maid there. We find out that she's loyal and capable, and that's pretty much all we need to know for the stage to be set.
Rising Action (Conflict, Complication)
A Woman with a Past
Even if she is just a maid, we find out in section two that Félicité was once in love with a guy named Théodore. He leaves her hanging though, and marries a rich woman, which breaks her heart. This complication is what leads her to quit her job and start working for Madame Aubain. It's a major turning point in her life, actually.
Climax (Crisis, Turning Point)
In section three heartache continues. This time Félicité's nephew, Victor, dies of yellow fever in Cuba. It's a huge loss for Félicité, but no one seems to care but her. On the other hand, when Virginie, Madame Aubain's daughter, dies, both women are heartbroken. It brings them closer together, and changes the whole dynamic of the story. Rather than looking forward to the future they are always looking back.
Section four brings a parrot into Félicité's life, a parrot that goes by the name of Loulou. He is her constant companion and causes her to catch a cold that leaves her deaf when he escapes one day and she searches for him out in the cold. When he dies she has him stuffed and starts to seem like a crazy lady. Madame Aubain dies, too, leaving Félicité alone with her dead bird.
Félicité dies alone in her impoverished bedroom, with a vision of Loulou greeting her from heaven. Everyone in the household has gone, and she's the last one guarding the place. She seems to have cared more than even the Aubain family about their home.