Here on Enotes you can read up on satire and how Wilde uses it as a literary device by going to The Importance of Being Earnest study guide and selecting "style".
A satire is the mockery of something serious. In Wilde's plays, the satire is often targeted to social conventions such as marriage, virtuous behavior, and courtship. Wilde is particularly enthusiastic about mocking the aristocrats, the upper classes, and their puritanical rules of social conduct which, to Wilde and many others, are utterly hypocritical.
Two important satires in the story are Wilde's attack on religious fanaticism in the character of Dr. Chausible, and his attack on virtuosity in the character of Miss Prism. These secondary characters are not often analyzed as thoroughly as Jack and Algernon, but their do reflect in full throttle Wilde's wish to completely ridicule the prudish Victorians.
Dr. Chausible is a kind but absent-minded man who is in charge of the parsonage of Jack Worthing's town. This would be the equivalent of a dioceses. The satirical aspect of Dr. Chausible is that, although he is a man of God and a leader of people, he is not at all very bright and fails to "get the point" in most of the observations that are made. He seems to be paying courtship to the very proper Miss Prism, who is the embodiment of concealed passions disguised as virtuosity. In Chausible, Wilde mocks the very people whom Victorians would look up to for advice and spiritual healing. If society were to depend on a man like Chausible, they would be in real trouble: How could you trust your fate to a man who can barely follow a conversation without missing the point?
Miss Prism, on the other hand, represents that Victorian righteous behavior that Wilde detests. She, a single and elder woman, is the governess of Cecily Cardew of whom Jack is guardian. Underneath her simple image we find a woman with an interesting past: She is not your average lady , for she confesses to be the author of a three-volume novel; she used to be Jacks's mother's governess and she is the person responsible of the loss of Jack, as a baby. She is the person who confuses the baby with her three-volume novel and places the baby inside her handbag while she places the novel in the perambulator!
Miss Prism is also overly judgemental, critical, mean, and somewhat vindictive when it comes to the actions of others. Her favorite phrase is "As they show, so shall they reap", which she says over and over to the amazement of Dr. Chausible. Yet, we also see a flirty streak when she speaks to Chausible and, in the end, is obvious that she has always had feelings for him.
Therefore, Wilde satirizes the Victorian insistence in being prudish and religious in two characters who, deep inside, are just as regular as anybody else, and maybe even less virtuous.