Algernon: Yes; but this isn't your cigarette case. This cigarette case is a present from some one of the name of Cecily, and you said you didn't know any one of that name.
Jack: Well, if you want to know, Cecily happens to be my aunt.
Algernon: [Retreating to back of sofa] But why does she call herself little Cecily if she is your aunt and lives at Tunbridge Wells? [Reading] "From little Cecily with her fondest love."
Jack: [Moving to sofa and kneeling upon it] My dear fellow, what on earth is there in that? Some aunts are tall, some aunts are not tall. That is a matter that surely an aunt may be allowed to decide for herself. You seem to think that every aunt should be exactly like your aunt! That is absurd! For Heaven's sake give me back my cigarette case. [Follows Algernon round the room.]
Algernon: Yes. But why does your aunt call you her uncle? "From little Cecily, with her fondest love to her dear Uncle Jack." There is no objection, I admit, to an aunt being a small aunt, but why an aunt, no matter what her size may be, should call her own nephew her uncle, I can't quite make out. Besides, your name isn't Jack at all; it is Ernest.
Jack: It isn't Ernest; it's Jack. (I.62-69)
Jack lies to cover up his double life. A simple white lie that he doesn’t know anyone named "Cecily" gets him into an incredibly messy situation. When he’s forced to admit he does know a "Cecily," he tries to pass her off as his aunt. But Algy, a fellow Bunburyist, eventually sniffs it all out and forces Jack to confess. What is most surprising is that Jack seems to have no shame about the lies he’s been feeding to Algernon for years.
Jack: […] When one is placed in the position of guardian, one has to adopt a very high moral tone on all subjects. It's one's duty to do so. And as a high moral tone can hardly be said to conduce very much to either one's health or one's happiness, in order to get up to town I have always pretended to have a younger brother of the name of Ernest, who lives in the Albany, and gets into the most dreadful scrapes. (I.83)
Jack reveals the reason behind his deceit. His life is torn between duty and pleasure. Being dutiful is excessively boring to Jack, so he created his younger brother, Ernest. With Ernest, he has a means of escaping the drab life of a legal guardian into the more interesting world of a social London.
Algernon: You have invented a very useful younger brother called Ernest, in order that you may be able to come up to town as often as you like. I have invented an invaluable permanent invalid called Bunbury, in order that I may be able to go down into the country whenever I choose. Bunbury is perfectly invaluable. If it wasn't for Bunbury's extraordinary bad health, for instance, I wouldn't be able to dine with you at Willis's to-night, for I have been really engaged to Aunt Augusta for more than a week. (I.88)
Bunbury is Algernon’s version of Ernest. Like Jack, Algernon also uses excuses about Bunbury to get out of familial responsibilities—like dining with his Aunt Augusta. He practices deceit, like Jack, to avoid unpleasant situations and create more pleasant ones for himself.
Cecily: Miss Prism has just been complaining of a slight headache. I think it would do her so much good to have a short stroll with you in the Park, Dr. Chasuble.
Miss Prism: Cecily, I have not mentioned anything about a headache. (II.21-22)
Cecily makes up false facts to get out of doing her lessons and to encourage a relationship between Miss Prism and Dr. Chasuble. The success of her deceit depends on her ability to read people; the fact that she does get Miss Prism and Dr. Chasuble to leave her is a testament to her powers of persuasion. Although her deceit is not as serious as Jack’s or Algernon’s, she lies for the same reasons—to get out of tedious or unpleasant situations. This makes her a perfect match for Algernon.
Cecily: Your brother Ernest…arrived about half an hour ago.
Jack: What nonsense! I haven't got a brother.
Cecily: Oh, don't say that. However badly he may have behaved to you in the past he is still your brother. You couldn't be so heartless as to disown him. I'll tell him to come out. And you will shake hands with him, won't you, Uncle Jack? (II.133-135)
The fact that Jack lied (and later revealed the truth) to Algernon gave the latter the opportunity to impersonate Ernest. Had Jack not lied, perhaps Algernon would never have had the chance to court Cecily as he did. As it stands, not only does Cecily believe in Ernest, but she's also on his side—scolding her Uncle Jack for being "so heartless as to disown him."
Jack: [Slowly and hesitatingly] Gwendolen—Cecily—it is very painful for me to be forced to speak the truth. It is the first time in my life that I have ever been reduced to such a painful position, and I am really quite inexperienced in doing anything of the kind. However, I will tell you quite frankly that I have no brother Ernest. I have no brother at all. (II.348)
An adept and habitual liar, Jack does not hold truth and honesty in high regard. Here, he comes out and says it. To him, lying is a more efficient and perhaps more noble way to live one’s life. This is, of course, the opposite of conventional thinking.
Algernon: [Stammering] Oh! No! Bunbury doesn't live here. Bunbury is somewhere else at present. In fact, Bunbury is dead. (III.49)
Interestingly, Algernon lies to free himself from future lying. By killing off the fictional Bunbury, Algernon is setting himself up to speak the truth for the rest of his life. He effectively lies so that he can live a better and more ethical life with Cecily.
Cecily: Well, I am really only eighteen, but I always admit to twenty when I go to evening parties.
Lady Bracknell: You are perfectly right in making some slight alteration. Indeed, no woman should ever be quite accurate about her age. It looks so calculating... (III.95-96)
The fact that Cecily admits to this white lie—concealing her true age—might show that she is not ashamed of telling a fib in the first place. But it also feeds into the stereotype that many women might try to seem younger and more beautiful in social situations. Here, Cecily wants to create the illusion that she is more mature, worldly, and perhaps more suitable as a prospective wife.
Jack: The Army Lists of the last forty years are here. These delightful records should have been my constant study. [Rushes to bookcase and tears the books out.] M. Generals... Mallam, Maxbohm, Magley, what ghastly names they have—Markby, Migsby, Mobbs, Moncrieff! Lieutenant 1840, Captain, Lieutenant-Colonel, Colonel, General 1869, Christian names, Ernest John. [Puts book very quietly down and speaks quite calmly.] I always told you, Gwendolen, my name was Ernest, didn't I? Well, it is Ernest after all. I mean it naturally is Ernest. (III.170)
This is perhaps the most ironic revelation of the whole play. It shows that Jack has not been lying this entire time to Gwendolen. His name really is Ernest. The pun comes into play. Jack has been earnest about being Ernest.
Lady Bracknell: My nephew, you seem to be displaying signs of triviality.
Jack: On the contrary, Aunt Augusta, I've now realised for the first time in my life the vital Importance of Being Earnest. (III.180-181)
Despite Jack’s statement that he’s learned the "Importance of Being Earnest" or the importance of being honest, we must question his sincerity. Because we realize that there is a pun between the adjective "earnest" and the proper name "Ernest," we can interpret Jack’s comment as tongue-in-cheek.
He was accidentally truthful in telling Gwendolen his name was Ernest. But he was still untruthful about his younger brother being named Ernest. So in this way, Jack is both earnest and deceitful for the duration of the play. So what does Jack mean here? The importance of being honest? Or the importance of being named Ernest?