Lady Catherine is a satire of a grande dame—a totally overbearing, domineering woman who has always gotten her own way and can't stand to have anyone disagree with her, like a less charming, early 19th-century Violet Grantham. At Rosings, she talks (and talks and talks):
without any intermission till coffee came in, delivering her opinion on every subject in so decisive a manner, as proved that she was not used to have her judgement controverted. She inquired into Charlotte's domestic concerns familiarly and minutely, gave her a great deal of advice as to the management of them all; told her how everything ought to be regulated in so small a family as hers, and instructed her as to the care of her cows and her poultry. Elizabeth found that nothing was beneath this great lady's attention, which could furnish her with an occasion of dictating to others. (29.11-15)
Lady Catherine is really more of a caricature than anything else. It's as though Austen took that one character trait—a love of "dictating to others"—and just ran wild with it. This lady came all the way from her estate just to tell Lizzy that she'd be "polluting" the "shades of Pemberley" by marrying Darcy (56.63). It's completely inappropriate and completely hilarious.
But we have to point out that the one financially independent woman in the whole novel (remember, she is a super-rich widow) is a horrible buffoon. Way unfair? Is Austen playing into stereotypes about how women and power shouldn't mix? Is there some other reason to have Lady Catherine in the story other than to give Darcy his own embarrassingly awful relative?