The central conflict of the this great play comes about because of Bunburying. According to Algernon, both he and Jack are "confirmed Bunburyists." Jack has no idea what he is talking about and either does the audience until Algernon explains that he has an imaginary friend who is very ill. This man's name is Mr. Bunbury, and whenever Algernon has a social obligation he would rather avoid, he claims that his good friend Bunbury needs his immediate help in the country. Once he we hear his explanation, we realize we are ALL Bunburyists. We have all made up excuses, blaming obligations to other people, to get out of social events, work, blind dates, etc.
Jack is also a Bumburyist. He generally lives in the country, and tells them that he has to deal with his brother Ernest in the city, and then when he is in the city, he says he IS Ernest. He too is creating an excuse to get out of obligations and the boredom of life in the country. Clearly, Jack is re-creating his whole identity with this deception. He gets to be a completely different person in the city.
That both of these men have gone to these extremes to give themselves social freedom makes an interesting point to the theme of the play. Are men seen as needing these kind of ruses to avoid the weight of society? Why can't or don't the female characters do the same thing? Do they, but in different ways? (ie. Cecily's "fictional" diary; Miss Prism's three-volume novel). That the men get caught and get away with the deceptions is also interesting. Does this play suggest the stereotype of the double standard for men and women -- that men can get away with a lot more than women without fear of how their actions will affect their reputations and their marriage prospects? Wilde's play is a brilliant satire, and these issues are at the forefront of what he saw as the flaws in English society.