Miss Fortini is Eilis' manager at Bartocci's Department Store, but she doesn't just teach Eilis how to fold clothes—she teaches her how to be a real American lady.
Unlike the crotchety Miss Kelly, Miss Fortini actually seems to be a good boss, one who treats all of her customers equally and respects her employees as human beings. In fact, Miss Fortini and Eilis eventually get so close that they regularly get lunch together, which not only provides Eilis with some great gossip but also some killer insight into American culture.
This is most evident when Miss Fortini helps Eilis find a bathing suit. Although this scene is hilarious for many reasons—Miss Fortini's insistence on seeing Eilis naked high among them—it's an important moment because Miss Fortini is making it her mission to guide Eilis through American social norms, which sometimes seem "utterly foreign in its systems and its manners" to Eilis (1.226).
It's a tough (and strange) job, but someone has to do it.