This is an example of direct address to the reader by an omniscient narrator, who offers facts, opinions, arguments, and moral judgements, and expresses themselves as a character, not just a conduit for the story. The technique of direct address was popular in the 18th and 19th centuries. Here are three examples spanning this period:
In our last book we have been obliged to deal pretty much with the passion of love; and in our succeeding book shall be forced to handle this subject still more largely. It may not therefore in this place be improper to apply ourselves to the examination of that modern doctrine, by which certain philosophers, among many other wonderful discoveries, pretend to have found out, that there is no such passion in the human breast.
Henry Fielding (1749). The History of Tom Jones, a Foundling, book 6, chapter 1. Project Gutenberg.
This state of things I have thought it necessary to premise for the information of the general reader, who might be apt to forget, that, although no great historical events, such as war or insurrection, mark the existence of the Anglo-Saxons as a separate people subsequent to the reign of William the Second; yet the great national distinctions betwixt them and their conquerors, the recollection of what they had formerly been, and to what they were now reduced, continued down to the reign of Edward the Third, to keep open the wounds which the Conquest had inflicted, and to maintain a line of separation betwixt the descendants of the victor Normans and the vanquished Saxons.
Walter Scott (1819). Ivanhoe, chapter 1. Project Gutenberg.
With a single drop of ink for a mirror, the Egyptian sorcerer undertakes to reveal to any chance comer far-reaching visions of the past. This is what I undertake to do for you, reader. With this drop of ink at the end of my pen, I will show you the roomy workshop of Mr. Jonathan Burge, carpenter and builder, in the village of Hayslope, as it appeared on the eighteenth of June, in the year of our Lord 1799.
George Eliot (1859). Adam Bede, chapter 1. Project Gutenberg.
Direct address was criticized in the early 20th century as an unrealistic approach that interfered with the reader’s suspension of disbelief, and it was largely abandoned by the mid-20th century, being replaced with the modern writing-class dogma of “show, don’t tell”. I wrote more about these events in this answer. But the writers who employed direct address had good reasons for doing so, which I enumerate below, based on the account by Wayne Booth in The Rhetoric of Fiction.
The efficient provision of facts.
The most obvious task for a commentator is to tell the reader about facts that he could not easily learn otherwise. There are many kinds of facts, of course, and they can be “told” in an unlimited number of ways. Stage setting, explanation of the meaning of an action, summary of thought processes or of events too insignificant to merit being dramatized, description of physical events and details whenever such description cannot spring naturally from a character—these all occur in many different forms.
Wayne Booth (1961). The Rhetoric of Fiction, p. 169. University of Chicago Press.
You can see this in the excerpt from Ivanhoe quoted above, which briefly and effectively sketches the relations between the English and the Normans. This kind of background information is hard to convey through action or dialogue, without resorting to expedients like “as you know, Ivanhoe, the distinction between the Anglo-Saxons and the Normans has persisted from the time of William the Second” that are more unrealistic than direct address.
Influencing the opinions of the reader.
If all this is true of fact, it is even more true of evaluative commentary. Indeed, most seeming facts carry, in fiction, a heavy load of evaluation. They order in some way the importance of the parts; they work on the beliefs of the reader.
Booth, p. 177.
This is what Fielding is up to in the excerpt from Tom Jones quoted above. The whole of this chapter is an argument intended to persuade the reader of the importance of love, a belief which is going to be necessary for the appreciation of the next part of the story. Fielding’s narrator concludes by saying that if you don’t agree then “you have, I assure you, already read more than you have understood; and it would be wiser to pursue your business, or your pleasures (such as they are), than to throw away any more of your time in reading what you can neither taste nor comprehend.” Again, it is much harder to attempt this kind of effect in the “show, don’t tell” style of narration, which has to take the reader’s beliefs as they come.
Making moral judgments.
If novelists must work hard to establish their norms, they often must work even harder to make us judge their characters accurately in the light of those norms. After all, there is a measure of agreement among us about the relative value of generosity, say, as opposed to meanness, or kindness as opposed to brutality. Though some of the terms for the four cardinal virtues may, like the word virtue itself, be in disrepute, the virtues themselves are still in high esteem. But like Socrates’ interlocutors, we do not agree about whether a particular action is wise, temperate, just, or courageous. Though our critical fashions do not favor talk about praising and blaming literary characters, many critical disputes still stem from our inability to agree on precise measures of praise and blame.
Booth, pp. 182–183.
This is a technique that Austen often uses, drawing the attention of the reader to fine distinctions of virtue and vice in her characters that might otherwise be missed. That’s one of the things that’s going on in the direct address from Pride and Prejudice quoted in the question: Austen’s narrator draws the reader’s attention to the fact that “the establishment of her children” has been Mrs. Bennet’s “earnest desire” and life’s work to accomplish, and though we, like the narrator, might wish that her success in this respect might make her “a sensible, amiable, well-informed woman”, such a dramatic transformation of her character is an unrealistic expectation. The narrator encourages us to observe the character’s faults but to understand their source, in her anxiety over the prospects for her daughters.
The provision of narrative interest. A substantial part of a novel consists of narration, and this needs to be interesting enough to keep the reader entertained. The usual ways to try to do this are through the continual introduction of events, or though the quality of the prose. But an author using direct address can make the narration interesting though the characterization of the narrator:
But we also see here [in Austen’s Emma] a beautiful case of the dramatized author as friend and guide. “Jane Austen” like “Henry Fielding,” is a paragon of wit, wisdom, and virtue. She does not talk about her qualities; unlike Fielding she does not in Emma call direct attention to her artistic skill. But we are seldom allowed to forget about her for all that. When we read this novel we accept her as representing everything we admire most. She is as generous and wise as Knightley; in fact, she is a shade more penetrating in her judgment. She is as subtle and witty as Emma would like to think herself. Without being sentimental she is in favor of tenderness. She is able to put an adequate but not excessive value on wealth and rank. She recognizes a fool when she sees one, but unlike Emma she knows that it is both immoral and foolish to be rude to fools. She is, in short, a perfect human being, within the concept of perfection established by the book she writes; she even recognizes that human perfection of the kind she exemplifies is not quite attainable in real life. The process of her domination is of course circular; her character establishes the values for us according to which her character is then found to be perfect. But this circularity does not affect the success of her endeavor; in fact it insures it.
Booth, pp. 264–265.