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.