In The Importance of Being Earnest, Oscar Wilde's use of epigrams (contradictory statements) is what anchors the comedic aspect of the play. Along with the use of epigrams, Wilde employs irony to drive the situations that twist the plot and that make the the dialogues and dynamics among the characters paradoxical.
The final phrase of the play,
I’ve now realized for the first time in my life the vital Importance of Being Earnest.
is an example of the use of irony and paradox to convey the opposite of what is going on.
Jack is never honest in the play. He never intends to tell anybody his real name until his fake persona is "found out", first by Algernon, and then by Cecily and Gwendolen. Claiming that his name is Ernest for his own convenience, he also lies, to his love interest, Gwendolen, and to Gwendolen's mother, Lady Bracknell.
He is dishonest to Miss Prism, Cecily and Dr. Chasuble telling them that he has a wicked brother in London named Ernest who causes havoc; that, for that reason, he has to go to London to solve Ernest's problems. This is a lie because the reason why Jack goes to London is "to become" Ernest, to run bills in restaurants, and to cause havoc with Algernon. This is why Algernon is shocked in Act I to find out that his friend Ernest's real name is Jack.
Additionally, he is dishonest when he falsely claims that his wicked brother Ernest died from "a chill". This, he does intentionally to end his double life and marry Gwendolen the proper way. Little does he know that Algernon already took the advantage by showing up in Jack's estate pretending to be "the wicked brother Ernest".
All this being said, the play ends with a shocking twist: Jack's real father's name is Ernest and, since Jack is his eldest son, Jack duly gets his father's name. This means that Jack, who lied about being Ernest and about many other things, overrules everything that he did and claims that, after all, he was telling the truth.
When Wilde uses the phrase "the vital importance of being earnest" he does it with two intentions: to point out the irony of the situation, to question the real value of truth versus falsehood. In Wilde's treaty The Decay of Lying, Wilde favors lying as a form of art. Aesthetics favor the fake versus the real; life should imitate art, and not the opposite. In true Wildean fashion, Jack does NOT learn the importance of being earnest. He actually admires the fact that his lying led nowhere, that providence rendered him truthful, and that there will be no consequence as a result of his lies because...they have turned into truths.