True romance has not changed substantially since Jane Austen's day. Men and women fall in love, are presented with obstacles, overcome obstacles, and pursue marital bliss with the same mix of tears, laughter and embarrassment as the recipe called for in Regency England. Which is why people continue to read a novel in many ways merely a provincial portrait of rural upper middle class Britain at the cusp of the 18th and 19th centuries.
There are other reasons, too. Austen knew how to write, certainly, and had an excellent (if sometimes too cultured) sense of humor, particularly regarding instantly recognizable character types. Which has led to unfounded suggestions of satirical intent—Austen's demure observations aren't intended for anything as politically motivated as satire, simply to show the foibles to which humans are prone.
And the difficulty of obtaining a good match. If there is a political element to Pride and Prejudice it's the idea that women of good character can secure men of good character, women of bad character will attract men of bad character, and sometimes unions are formed that are not altogether good or bad but are expedient. Elizabeth Bennet's good fortune is that marriage to Mr. Darcy is both expedient and good.
In many ways this is simply a fun love story with enough ups and downs and twists to make it interesting. It's funny, and the dialogue really is some of the best of its day and still holds up 200 years later. Not much happens, but as a "novel of manners" not a lot is expected to (though not all readers will be able to identify with a landed gentry whose time is equally divided between balls and leisure).
The real value of Pride and Prejudice, however, is not the love story. Long before the "psychological novel" Austen was investigating human emotion and motivation on a serious level. Her genius lay in her ability to evoke psychological elements through external observations alone—she describes behavior, not thoughts. This novel clearly demonstrates her talent, and is largely responsible for the fairly recent Austen revival.