The film is about coming into one's identity. Jack is known as Ernest while he is in London, and he wants to marry Gwendolen who belongs to a family of high status. In order to do so he must prove to her mother that he and his family are worthy--of quality standing--to marry.
Jack has hidden his true identity as he believes that Gwendolen won't marry him if she discovers his name is Jack. In fact, she says Ernest has a musical quality to it and she knew she would marry someone named Ernest, but Jack has no such quality. Oscar Wilde uses this as a metaphor for the harshness of classes opposes anyone trying to get in from a lower ranking. Thus, Gwendolen saying she wouldn't marry a man named Jack has bigger implications in the underpinnings of the story as it relates to the class structure in Britain.
We also see that character is something that everyone attempts to keep polished in the public eye, but behind closed doors people are quite different. Wilde again makes a point about British society caring most about the appearance of a person rather than the quality of his heart as one could have an average character but be in high standing with society so, will always be in high-standing.
Asquith shows us that the process of courtship pulls out all the stops in that in order to marry you are scrutinized to every detail. And, thus when Jack is found to not be suitable it is ironic as once his true identity is revealed he is in fact the cousin of Lady Bracknell. The same woman attempting to stop his engagement to her daughter.
