The prime function and purpose of Kristine in this play is the way that she acts as a foil to both Jean, her fiance, and Julie, her mistress. She has the role of being the Count's cook and is marked by her acceptance of the role that she has in society and the way in which she never seeks to transcend that role or fight against the sphere that she has been given by society.
One way that this is shown is through her extreme traditionalism. She is deeply religious, and finds the actions of Julie very offensive and horrendous. For example, when she discovers that Jean and Julie have slept together, Kristine says that she is no longer able to work for such an employer who flouts all moral standards. Interestingly, she places the majority of the blame firmly on the shoulders of Julie and tells Jean that his behaviour would have been not as bad if he had slept with another servant. From Kristine's perspective, as class-bound as she is, it is Julie who has debased herself by sleeping with a servant. She is instrumental in denying Jean and Julie escape, showing her ultimate loyalty lies with the Count rather than anybody else.