Some scholars argue that Pride and Prejudice, which Austen wrote in the late 1790s as First Impressions, was originally an epistolary novel. Epistolary was a popular form in the eighteenth century. It is a type of novel consisting entirely of an exchange of letters between different people. Austen's draft novel Lady Susan is epistolary.
While we do not know if Pride and Prejudice was originally composed as a series of letters and later reworked because of changing fashions, letters play an important role in the novel and are primarily used to communicate background information. For instance, after Elizabeth turns down Darcy's marriage proposal in a fit of rage because he is so arrogant and because he admits to having tried to break up Jane and Bingley, he writes her a letter explaining his position. The letter provides a counter-narrative to Elizabeth's accusations from Wickham and explains that he, Darcy, truly did not think Jane cared much for Bingley.
Later, letters inform Elizabeth of the devastating news of Lydia's elopement with Wickham. Mrs. Gardiner, writing from London, offers background information about Lydia that reveals that Lydia is as unrepentant as ever. Mr. Collins's chiding letter about Lydia, in which he says he is now glad he didn't marry into the family, shows what a jerk he continues to be.
The letters may or may not be remnants of an earlier draft, but they do provide important information about events and characters.