Hildebranda Sánchez is, for most of the novel, Fermina Daza's only friend. She's also her cousin. Fermina doesn't get out a lot.
Hildebranda and Fermina find themselves in a similar situation in their teens – they're both in love with men that their families don't approve of and carrying on secret love affairs via telegram. Hildebranda is slightly more sophisticated than her cousin and is always two steps ahead of Fermina when it comes to trying daring things like smoking and flirting with men. This causes the two to butt heads from time to time (Fermina even calls Hildebranda a whore at one point for flirting with Dr. Urbino), but eventually Fermina ends up following Hildebranda's example. It seems that Hildebranda's flirting with the doctor, after all, is what prompts Fermina to agree to date him.
Hildebranda is the one who provides a place to stay for Fermina when she fights with her husband. Hildebranda as an old woman makes Fermina aware of how much they have both aged, but she's also the one who reminds Fermina of her youth by showing her old photographs and laughing with her about the good old days.