This is a great question. As in all great works, this work has many important themes. The most prominent theme is the theme of love. We can say that the whole work can be seen through the lens of love between Darcy and Elizabeth. In addition, what makes this story great is that the two individuals have to overcome many hurdles to get together. For example, Elizabeth has to overcome her prejudice against the poor first impression of Darcy and her strong dislike of the arrogance of the upper-class. Darcy has to get over his class consciousness and his feeling of being superior to be able to see the great qualities of Elizabeth. As the story progresses, there is character development in the true sense of the word, as they shed their prejudices and fall in love. Other themes are: class, courtship, and the importance of reputation in a hierarchical society.
As for the question of whether this story is applicable to today's customs, I would say yes. Whenever you cross any social boundary, there will be blind spots, prejudices, and various other hardships. If you are able to find love within in this context, it is beautiful. You would have a modern day Pride and Prejudice.
As said in the words of Mary at the beginning of the novel, "human nature is particularly prone to [pride]" (Volume I, Chapter 5). In the novel, pride prevents the characters from seeing the truth of a situation and from achieving happiness in life. Pride is one of the main barriers that creates an obstacle to Elizabeth and Darcy's marriage. Darcy's pride in his position in society leads him initially to scorn anyone outside of his own social circle. Elizabeth's vanity clouds her judgment, making her prone to think ill of Darcy and to think well of Wickham. In the end, Elizabeth's rebukes of Darcy help him to realize his fault and to change accordingly, as demonstrated in his genuinely friendly treatment of the Gardiners, whom he previously would have scorned because of their low social class. Darcy's letter shows Elizabeth that her judgments were wrong and she realizes that they were based on vanity, not on reason.
Pride and prejudice are intimately related in the novel. As critic A. Walton Litz comments, "in Pride and Prejudice one cannot equate Darcy with Pride, or Elizabeth with Prejudice; Darcy's pride of place is founded on social prejudice, while Elizabeth's initial prejudice against him is rooted in pride of her own quick perceptions." Darcy, having been brought up in such a way that he began to scorn all those outside his own social circle, must overcome his prejudice in order to see that Elizabeth would be a good wife for him and to win Elizabeth's heart. The overcoming of his prejudice is demonstrated when he treats the Gardiners with great civility. The Gardiners are a much lower class than Darcy, because Mr. Darcy is a lawyer and must practice a trade to earn a living, rather than living off of the interest of an estate as gentlemen do. From the beginning of the novel Elizabeth prides herself on her keen ability for perception. Yet this supposed ability is often lacking, as in Elizabeth's judgments of Darcy and Wickham.
Considerations of class are omnipresent in the novel. The novel does not put forth an egalitarian ideology or call for the leveling of all social classes, yet it does criticize an over-emphasis on class. Darcy's inordinate pride is based on his extreme class-consciousness. Yet eventually he sees that factors other than wealth determine who truly belongs in the aristocracy. While those such as Miss Bingley and Mrs. Hurst, who are born into the aristocracy, are idle, mean-spirited and annoying, Mr. and Mrs. Gardiner are not members of the aristocracy in terms of wealth or birth but are natural aristocrats by virtue of their intelligence, good-breeding and virtue. The comic formality of Mr. Collins and his obsequious relationship with Lady Catherine serve as a satire class consciousness and social formalities. In the end, the verdict on class differences is moderate. As critic Samuel Kliger notes, "It the conclusion of the novel makes it clear that Elizabeth accepts class relationships as valid, it becomes equally clear that Darcy, through Elizabeth's genius for treating all people with respect for their natural dignity, is reminded that institutions are not an end in themselves but are intended to serve the end of human happiness