Jane Austen's Emma has a great deal to offer to the modern audience because Emma is a modern character.
This is most certainly the case with other of Austen's protagonists as well because Austen was something of a paradox in her time. She was a proper young woman, the daughter of a clergyman, who wrote with skills no one around her knew she possessed—her novels were written in secret, and printed anonymously. However, Jane's protagonists were believable and appealing to her audiences. They were strong, determined women: however their mistakes and/or failures kept these figures grounded in reality. Austen's characters were smart and witty, and somewhat ahead of their time, but this is also the case with Austen herself: for female authors were considered an anathema in the culture in which she lived.
...many of Austen’s works went to print with no name on the title page to avoid linking her to the negative stigma of female authorship.
In the novel, Emma has been carried away by a sense of accomplishment that she seems not to possess: she takes credit for making a match between her former governess, Miss Taylor, and the man she marries, Mr. Weston. With this seemingly inaccurate perception of her own abilities, Emma goes about trying to arrange a match for her new friend, Harriet Smith, but after repeated attempts, the men she has in mind for Harriet do not ask for her hand, but actually end up engaged to someone else.
An example of her attempt at such a match is seen with Mr. Elton, the first man Emma decides Harriet will marry. As they are all gathered together reading small pieces of literature, Emma prompts Mr. Elton to offer:
…enigmas, charades or conundrums, that he might recollect…
Emma prompts Elton to write something of his own, but he declares he is unable to do so. However, the next day he returns with something "a friend" wrote, and offers it as a piece to add to the collection of writings that Harriet is gathering. He notes:
Being my friend's I have no right to expose it in any degree to the public eye, but perhaps you may not dislike looking at it.
Emma is certain that Elton has written it himself, and upon his departure, she prompts Harriet to take it, although Harriet is too shy to do so:
"Take it," said Emma, smiling, and pushing the paper towards Harriet, "it is for you. Take your own."
But Harriet was in a tremor and could not touch it…
Emma takes it upon herself to do so, and in general goes about promoting the relationship until Mr. Elton, alone with Emma in a carriage, takes hold of her and tries to "make violent love to her." This is the first relationship that Emma tries to arrange for Harriet that falls flat. Later, news arrives that while traveling, Mr. Elton has become engaged to another young lady.
This process is repeated more than once. However, it is Emma's timeless "human condition" that makes this novel appealing to a modern audience: the idea of one friend trying to "fix up" another with someone the first knows, the sense of the best intentions going awry, and, ultimately, a person's ability to learn and prosper from his/her own mistakes, offer Emma as a timeless piece of literature that is perhaps even more appealing today than when first written in that it also captures the charm of an age, long past.