Lady Catherine de Bourgh is haughty, egotistical, and domineering. Because of her wealth and social standing she believes she can command anyone around her. People such as Mr. Collins contribute to this personality by acting as sycophants who bow to her every command. Her nephew Darcy initially does whatever his aunt requests out of respect for her, but by the end of the text, he makes the choice to go against her wishes and marry Elizabeth.
One of Austen's recurring themes was the role of money in society. She uses Lady Catherine de Bourgh as a symbol of the uppercrust of society who wield their money with social power. It would have been extremely unusual for Elizabeth to have been allowed to marry Darcy because of her low social and financial standing.
Lady Catherine is also demanding, inconsiderate, and meddlesome. It is very clear that she consistently intrudes into Mr. Collins's private affairs, despite the latter's protestations otherwise:
She had even condescended to advise him to marry as soon as he could, provided he chose with discretion; and had once paid him a visit in his humble parsonage, where she had perfectly approved all the alterations he had been making, and had even vouchsafed to suggest some herself—some shelves in the closet up stairs.
Mr. Collins tries to couch Lady Catherine's actions in complimentary terms, but it is obvious that Lady Catherine enjoys manipulating people for her pleasure. In modern terms, we would say that Lady Catherine suffers from a narcissistic personality disorder. She has an inflated sense of her own importance and does not hesitate to enlighten others about what she perceives are their shortcomings. Despite her overpowering personality, however, Lady Catherine is extremely sensitive to criticism. These are the classic symptoms of someone suffering from such a disorder.
We see Lady Catherine's nature clearly in her conversation with Elizabeth. She tries to ride roughshod over Elizabeth, but as we can see, Elizabeth refuses to be intimidated:
"Because honour, decorum, prudence, nay, interest, forbid it. Yes, Miss Bennet, interest; for do not expect to be noticed by his family or friends, if you wilfully act against the inclinations of all. You will be censured, slighted, and despised, by everyone connected with him. Your alliance will be a disgrace; your name will never even be mentioned by any of us."
"These are heavy misfortunes," replied Elizabeth. "But the wife of Mr. Darcy must have such extraordinary sources of happiness necessarily attached to her situation, that she could, upon the whole, have no cause to repine."
From the above, we can see that Lady Catherine is used to getting her own way. Thus, she experiences great shock when Elizabeth deflects her accusations and dispels her spurious arguments skillfully.