There are many female characters in this novel who play a number of very different roles, but in general, the role of all women in the Regency culture Austen describes is to get married. This pressure to marry drives much of the novel's plot.
For example, the eldest Bertram daughter, Maria, is pushed to marry a ridiculous man, whom she does not love, because of his wealth and position in society. Likewise, Fanny Price is pressured to marry Henry Crawford, an immoral man she does not love, because marrying him would be such a step upward for this penniless relation.
On one level, the novel contrasts the fate of Maria, who marries for all the wrong reasons and comes to a bad end, with Fanny, who sticks to her principles and will not marry a bad man for wealth and status. She is punished with exile from Mansfield Park but then rewarded with the man she truly loves, her cousin Edmund.
Women in the novel are deformed in different ways through the marriage market. Mary Crawford loses Edmund, the man she loves, because she fears she will not have a high enough position in society as the wife of a clergyman, while Maria ends up having a scandalous affair, and Lady Bertram turns out to be helpless and indolent in her wealthy marriage. Rather than receiving a sensible education and sensible moral guidance, women are shown being expected to marry for all the wrong reasons and given no reasonable alternatives to marriage. As in her other novels, Austen condemns a marriage market that pressures women not just to marry but to marry for money and position rather than for love.