The genre classified as "domestic fiction" became popular from the early to mid 1800's and is also found under categories such as "women's fiction", or sentimental fiction.
This type of literature is characterized for centering the plot around a young woman, often in distress, and unable to solve her main problems due to the unequal social adequacy of women. According to Nina Baym, who wrote Woman's Fiction, this genre can be defined as
...the story of a young girl who is deprived of the supports she had rightly or wrongly depended on to sustain her throughout life and is faced with the necessity of winning her own way in the world . . . . At the outset she takes herself very lightly--has no ego, or a damaged one, and looks to the world to coddle and protect her . . . .To some extent her expectations are reasonable--she thinks that her guardians will nurture her . . . But the failure of the world to satisfy either reasonable or unreasonable expectations awakens the heroine to inner possibilities. By the novel's end she has developed a strong conviction of her own worth as a result of which she does ask much of herself. She can meet her own demands, and, inevitably, the change in herself has changed the world's attitude toward her, so much that was formerly denied her now comes unsought
This being said, there are plenty of themes that are completely in tandem with this definition. In Pride and Prejudice more than one female is completely dependent on the expectations that society bestows upon them. In this novel, women depend on marriage to rise and survive in society, yet, their social status impede them from being able to marry the way they wished. Additionally, an entailment placed upon the family makes the women destitute upon the death of their father since there are no male heirs that can legally inherit. This means that men were the only people in society with the right to own property.
If you can put yourself in their situation, it would be very hard to comprehend how society can just decide who is worthy and who is not; who has the right to freedom and joy and who doesn't.
Hence, Pride and Prejudice epitomizes the meaning of domestic, sentimental fiction.