This very poignant moment in the story is a battle of the wills: The totally opposite and opposing Lizzie and Lady Catherine go mano a mano on making their point supersede the other one's all over Mr. Darcy
Lady Catherine had promised her daughter that Mr Darcy would be her husband. Then she hears that Darcy was going to propose to Lizzie. She confronts Lizzie, and Lizzie shows what she is made of.
Some additional roles of this conversation are:
To show the signs of changing times: The story is actually set in changing times in England. While the old traditions were still kept abreast, the reality is that Lizzie's society was approaching the Victorian era, in which more and more independent women would talk like her and have the same opinions. Lizzie is Austen's own mind and mouth in print.
To establish the lack of wit of the aristocracy: This show of words showed that Lizzie, the common, red-blooded, middle-class, simpleton that Lady Catherine looked down on was more intelligent and equipped for life than Lady Catherine.
To entertain like the previous poster said, Elizabeth's wit was deserving of a show of force of this magnitude. In a time when the aristocracy was viewed with the same fanaticism as Mr. Collins would express, what Lizzie did was something thought of almost unreal and socially unthinkable- to diss her out like that.
To voice the opinions of the audience: Jane Austen was sincere in voicing out what everyone else thought: That the aristocracy was an idle and clueless class of people with no touch with reality; that not enough opportunities of expression were given to women and other social classes, and that society was itself wrong in its rules and antiquated regulations against women, and people without means.