Mrs. Norris is the kind of relative that you attempt to hide from at family reunions. The woman is pretty awful and is the most easily identifiable antagonist in the novel. And in a story where characters often refuse to fit into clear-cut roles, this is something of a relief.
The narrator seems to feel this, too, because it's pretty much open season on Mrs. Norris from the start. No one needs to feel bad about making fun of Mrs. Norris because she pretty much has it coming. The woman is judgmental, rude, and totally oblivious. She spoils the nieces (Maria and Julia) who clearly don't respect her at all and mistreats the niece (Fanny) who would probably be even nicer to her if Mrs. Norris bothered to treat her well. Mrs. Norris is also hilarious in a cringe-worthy way and often provides some much-needed comic relief in a novel that tends towards the serious at times.
One of Mrs. Norris's funniest rants comes right after Sir Thomas returns from Antigua and threatens to take away her World's Best Chaperone mug. Or something like that. Mrs. Norris's account of a trip goes on and on until a ludicrous conclusion:
And then the poor horses too! To see them straining away! You know how I always feel for the horses. And when we got to the bottom of Sandcroft Hill, what do you think I did? You will laugh at me – but I got out and walked up. I did indeed. It might not be saving them much, but it was something, and I could not bear to sit at my ease, and be dragged up at the expense of those noble animals! I caught a dreadful cold, but that I did not regard. (20.5)
We're surprised that Mrs. Norris didn't carry the horses up the hill herself. Mrs. Norris is a big fan of something called hyperbole, which is a fancy word meaning exaggeration.
Mrs. Norris is definitely good for a laugh, but she has some serious elements to her as well. She holds a lot of snobby social views that give us an idea of how important class and social rank are in this world. Her rude treatment of Fanny is clear evidence of this. She feels that Fanny is somehow "less" than Maria and Julia Bertram because her birth family is poor.
But Mrs. Norris isn't some sort of evil super-villain. Sir Thomas probably explains this best: "Sir Thomas indeed, was, by this time, not very far from classing Mrs. Norris as one of those well-meaning people who are always doing mistaken and very disagreeable things" (33.19). Mrs. Norris causes a lot of problems and is often the butt of jokes in the novel, but she isn't totally lacking in some sympathetic and serious aspects.