OK, most difficult things first: though we'd be hard pressed to simply label Austen's novel a work of satire, her writing is heavily satirical throughout. Her deadpan humor and biting send ups of the characters we encounter gleefully skewer typical social types of her day (that are still recognizable in our own society). Austen's dryly comic commentary on figures like the snobbish John and Fanny, gold digger Lucy, and rumor mongering Mrs. Jennings clearly paint a picture of society as Austen saw it – and it's quite hilarious. In a broader literary sense, the novel also satirizes the novels that immediately precede it (what's commonly called the novel of sensibility, or the sentimental novel), represented by the melodramatic swoons and mood-swings of Marianne Dashwood.
However, there's more to Sense and Sensibility than a collection of caricatures. At the novel's heart is a truly moving story about family and love. As a romance, we sympathize with the characters profoundly, even when we recognize that they're being ridiculous. The love plots are what drive the novel from start to finish, and we can't be happy until they're resolved at the end.
Speaking of movement from beginning to end, this story is also about coming of age – not just for Marianne and Elinor, but also for Edward and, to a degree, Willoughby. The changes and development we note in the characters as they move through Austen's world are all extremely significant, and we see them grow from stereotypes into real people as they develop. Finally, to speak in rather abstract terms, it's also kind of a coming of age for the novel – Austen intentionally moves us away from the earlier models of "women's" fiction, and challenges us to look beyond the extreme emotionalism of earlier works, towards a new kind of writing about the private lives of women.