What is the role of the conversation between Elizabeth and Mr. Collins in chapter nineteen of Pride and Prejudice?

This rather awkward and comedic scene between Elizabeth
and Collins serves to reveal even more about Elizabeth's nature and character.  We learn
several very important things about her.  In this scene, Mr. Collins proposes; he is a
respectable man with a respectable position in life, and marrying him would be a
fortunate match for the poor Elizabeth, and serve to take her off of the hands of her
parents.  Her mother expects the proposal, and heartily hopes that Elizabeth agrees. 
Agreeing would also solve the stressful situation of the family money, since Collins is
a benefactor.

So, Elizabeth has pressure from her family,
from society, and from her own sense of duty and obligation all weighing on her response
to this proposal.  However, despite all of this, she refuses, because she simply can't
stand the man.  This reveals two important things about Elizabeth.  She is highly
independent, and stubbornly acts on her own feelings of right and wrong, along with her
own feelings on romance and love.  She is willing to risk being an old maid, and living
forever at her parents' house, then spend a lifetime with someone that she cannot love
or respect.  It is a risky endeavor; as Mr. Collins so indelicately puts it, it's not
like she can expect a proposal from someone better, given her family's circumstances. 
Secondly, we learn that for her to marry, she must love and respect the man.  She puts
love and respect above all else, and clings to it, even in the face of loneliness and
possible burdens on other people.  Unlike her more practical friend Charlotte, who
accepts Collins so that she won't burden her family anymore, Elizabeth wants more, and
holds out for real happiness.

Elizabeth is a strong-willed
and independent female, who risks all to ensure her own happiness.  In Jane Austen's
time, females like that were few and far between, and often looked down upon by
society.  Liz's conversation with Mr. Collins in this chaper reveals quite a bit about
her character and personality.  I hope that helped; good luck!