One reason why Jane Austen's characters make Pride and Prejudice such an everlastingly popular book is that each character is actually very realistic. While a lot of the characters are made to be humorous, none are caricatures; all are people everyone meets at least once in one's life. Beyond that, the genuine goodness and nobleness of heart that we find in the main characters also make the book particularly appealing.
While Elizabeth has her faults, namely being far too strong willed and far too quick to judge, she is a genuinely caring soul. Genuine concern for her sister Jane incites her to trek three miles across the country after a rain, arriving at Netherfield unfit to be seen in society. Genuine care and concern for her family, upon hearing that Lydia had run off with Wickham, incited her to return straight to Longbourn, ending early her summer trip through Northern England with her aunt and uncle Gardiner. Genuine concern for Lydia and her family also made her "burst into tears" before Mr. Darcy as she relayed to him Lydia's news when he came to call upon her at the inn (Vol. 3, Ch. 46). From these things alone we can see that, not only is Elizabeth characterized as a realistic person, she is characterized as a truly caring person.
Similarly, while Mr. Darcy has his faults, he is also characterized as a genuinely caring and noble person. For example, he genuinely loves Elizabeth despite her faults and poor upbringing, plus he sacrifices himself to save Elizabeth's reputation as well as her family's by bribing Wickham into marrying Lydia. We especially see how much he cares for her when he comes upon her in the inn after she had read the letters from Jane about Lydia, saying, "Let me call your maid. Is there nothing you could take, to give you present relief?--A glass of wine;--shall I get you one?--You are very ill" (Vol.3, Ch. 46).
In addition, while characters like Mrs. Bennet and Mr. Collins are extremely humorous and seem absolutely absurd, if we take a closer look we see that even those characters are representative of real people. There truly are ridiculous, vain mothers in this world who give their daughters poor guidance; and, there truly are clergyman or like-minded individuals who are also vain and arrogant.