The first sentence of the book is among the most famous lines in literature. What is its purpose?

Yes, this is a famous line. Really it provides the plot framework for the entire book. In a society where social stature and money are primarily held by a small minority of men, “single men in possession of a good fortune" become a sought after commodity for women. Nineteenth-century marriage was more about social and economic advantages rather than anything else. If rich men were "in want of a wife,” certainly young single women were in want of a rich husband!