Because Mrs. Bennet has only daughters, none of them can inherit the family estate, it will instead go to a distant cousin. It chafes her pride that she may potentially have to live with relations as a "poor relation" in her old age if her daughters do not marry and Mr. Bennet passes before her. It is vital to Mrs. Bennet to see her daughters married well, that is her main driving force in the book and she will stop at nothing (including socially embarassing herself and her daughters) to try to achieve this goal.
It can be argued that Mrs. Bennet favors Lydia who reminds her of herself, as Lydia is rather silly and boy crazy. Mrs. Bennet allows Lydia more liberties than she should because Lydia is too irresponsible to handle them and proves this when she gets herself in a situation that requires marriage to avoid complete social ruin.
Mrs. Bennet does not favor Elizabeth as she is more like her father and very head strong and sensible. Elizabeth thwarts Mrs. Bennet's plans to marry her tiresome cousin who would inherit the family estate which would make Mrs. Bennet's life easier and initially thwarts her plans to marry Darcy as well. Their relationship is much more adversarial.