This is Blanche Ingram speaking, the woman Jane thought Mr. Rochester would marry. This is a very uncomfortable moment for Jane, as Blanche is speaking about governessess, in the middle of a party in which they are both in attendance. Essentially, Jane has to sit with her student and listen to supposedly upperclass womendiscuss how they "know the faults of her class"-meaning Jane.
This is yet another example of class conflict in the book, and the hypocrisy/downright cruelty of the upper class in the society. This is not the first time Jane has experienced such blatant discrimination; it began when she was an orphan in the Reeds' household. Since then, her life has been a continuous cycle of oppression and contempt based on her social class. While Bronte is criticizing this aspect of the culture, it is important to note that Jane only becomes truly whole when she is independently wealthy. This may suggest something about the state of working class women at the time.