Mrs. Sparsit is Bounderby's middle-aged housekeeper. She was born into money and a high ranking family. Bounderby loves to play up this history. She is jealous of Louisa and, after Bounderby and Louisa are married, Mrs. Sparsit looks for any opportunity to bring Louisa down.
What exactly does a house-keeper do? Well, a rich, middle-class man like Bounderby couldn't really be bothered with his house, which would usually have had a bunch of servants doing the things that we have electrical appliances for. The person who managed the servants was either a wife, or in the case of a single man, a female housekeeper. The housekeeper was crucial to a well-run household, but her ambiguous rank in the house could cause a lot of problems. Think about it – what exactly is such a woman's position? She's kind of a wife, because she only works in a house where there is no wife. But, she's also kind of a servant – she can be fired, while a wife can't be gotten rid of that easily. She is higher in rank than the servants because she orders them around, but she is still lower than the house owner because he pays her a salary. So, what exactly is her rank and station? No one quite knew, and so there's lots of confusion and resentment whenever a housekeeper is in the picture. (Actually, same goes for governesses – check out Jane Eyre and Vanity Fair.)
That said, Mrs. Sparsit is a housekeeper with her eyes squarely on the prize. She wants to marry Bounderby and become a wife. Bounderby, on the other hand, has his eyes set on the bragging rights of having Mrs. Sparsit as his servant. Just as he makes up his own background, he gradually invents hers, telling everyone that she comes from the noblest of the nobility. Therein lies the confusion we mentioned. Now for the resentment. After Bounderby marries Louisa, Mrs. Sparsit makes it her mission to undermine and destroy the marriage and to catch Louisa in the act of adultery.
At the same time, Mrs. Sparsit is one of the more comic characters, useful for lightening the mood every now and again in this bleak novel. But, truthfully? Tastes in humor change over time. So, take it from us when we say that the scene of Mrs. Sparsit hauling Mrs. Pegler along is meant to be super hilarious.