In Pride and Prejudice, Jane Austen uses gender and character to both express the social norms of her time and to emphasize that there are more variations on character than society chooses to recognize. The Bennett sisters define the whole of female society. There is Jane, the incomparable beauty, who should be able to secuure a worthy suitor without ever opening her mouth. Then there is Elizabeth, very intelligent, independent and quick witted. She, it is thought would not secure a eligible suitor, her beauty being average, once she opened her mouth, men would run away from her fierce opinions and strong mindedness. Lydia, a silly girl given to spontaneous decisions fell into trouble, she should have been watched more closely by Mrs. Bennett, who is a caricature rather than a real mother. Mary, the studios one, will never marry and Kitty, too young, but expected to be able to secure a husband of some means. Mr. Darcy is the rich, indignant, handsome, austere gentleman who one would never expect to find Elizabeth Bennett attractive. You expect him to choose a wife based on social standing and breeding alone. Bingley, although not as rich as Darcy, but still well off, is looking for love. Mr. Wickham is a cad and a rouge, who is looking for a wife who has a rich purse. Mr. Collins, the minister, needs a wife, any wife. Jane Austen paints her characters in broad strokes.
This question could take pages to answer, but I will focus on the Bennett family to give you a brief look at how deeply gender and characterization are dealt with in this novel. Austen depicts Elizabeth as a bold, intelligent woman who easily and openly expresses her opinion on various subjects from marriage to family. However, Elizabeth's mother and younger sisters tend to fall into the stereotypical feminine role during this time - meaning that they were more concerned about appearing beautiful and important and impressing others than truly making themselves happy. Elizabeth's older sister wishes she could be more like her determined sibling, but she too is unable to articulate her feelings as easily as Elizabeth. In the end, the girls all find some sense of happiness - thanks primarily to Miss Elizabeth Bennett.