Oscar Wilde's A Woman of No Importance follows the tradition of Wilde's comedies of manners. This is a specific theatrical genre that aim to critique and even satirize the common dynamics of everyday Victorian society, emphasizing in the upper and middle classes.
The reason why these kinds of theatrical pieces exist is because, during the mid 1800s (to be specific to the Wildean tradition), the newly-created Victorian society experience a conversion in society that allows for more people to become "well-to do". The problem with that is that these very persons, all of a sudden, begin to act prudish, "holier than thou" and quite judgemental. For this reason, Wilde and many others who share his disdain for a hypocritical Victorian society come up with plays that reflect those silly behaviors. He takes the upper-hand at the fact that he is witty enough and brilliant enough to mock them completely without they even realizing it. After all,the well-to-do Victorians were Wilde's patrons!
In A Woman of No Importance we see the so-called "good people" of the upper classes hiding a secret: The very virtuous Mrs. Arbuthnot and Lord Illingworth have a child together, which is her deepest secret. However, this secret may cost because Lord Illingworth crosses paths with him and makes him his secretary. The secrets that continue to be expose will become the meat of the play and what ultimately allows Wilde to continuously beat his characters' prudish nature until the end.
Therefore, Wilde criticizes the hypocrisy of being charitable and virtuous while hiding an illicit affair, the reality of illegitimate children among the upper classes, the nepotism of the aristocrats in always defending their own, and the overall behaviors and mannerisms of those who call themselves better than anybody else.
A Woman of No Importance is a play by Irish playwright Oscar Wilde