This is a very important question because the notion of class is one of the most important themes in Jane Austen's Pride and Prejudice. Often, when people discuss the dynamic of class in the book, they reference Darcy's "upper class" mixing with Elizabeth Bennet's "middle class" status. However, while this comparison is neat and tidy, it's not really accurate. Mr. Bennet is actually an upper class gentleman and, although his fortunes seem to be declining somewhat, that would also make his daughters members of the upper class. That said, Mrs. Bennet does comes from a lower, more middle class background. This is not to say that her family is poor by any means; rather, it just means that Mrs. Bennet's relatives actually have to work for a living, while upper class gentlemen like Mr. Darcy enjoy inherited fortunes and lives of leisure. Even so, the Bennet family is actually upper class, although Mrs. Bennet's more middle class background complicates this status somewhat.
In any case, one of the ways in which Jane Austen realistically portrays the middle class is by showing how anxious the middle class is to prove its worth to the upper classes. As we all know, Mrs. Bennet (who has married into the upper class, but has a more middle class background) is anxious that her daughters marry and make "good matches." A "good match" would involve marrying a man of considerable fortune and reputation (a man, in other words, from the upper class). By pushing her daughters to marry such men, Mrs. Bennet hopes not only to have her daughters provided for, but also that they will finally be fully accepted into the elite social circle which they are technically already part of, but still somewhat tenuously connected to. In this way, Austen is showing the ways in which people of middle class backgrounds are anxious to be accepted by the snobbish upper class.
It's worth noting that, in representing this middle class anxiety, Austen's also trying to deconstruct the rigid notions of class in the first place. After all, the middle class characters in the novel are usually presented as financially stable, and even prosperous. However, because their wealth comes from work, rather than inheritance, the elite class persists in rejecting the "newly rich." By illustrating how frivolous this idea is, Austen creates a brilliant, satirical commentary on England's class structure.