In Oscar Wilde's satire of British social mores, The Importance of Being Earnest, Lady Bracknell is the play's central personification of England's enduring obsession with socioeconomic status and the upper stratum's snobbish perspectives of those less fortunate. She is also, however, superficial and autocratic without actually having a clue regarding the machinations of those around her. It is her snobbishness, though, that provides for the play's main conflict, as Jack must prove himself worthy of Gwendolen's hand while continuing to present himself as his more playful alter-ego, Ernest. Early in the play, Gwendolen informs Lady Bracknell that she is to be married to "Ernest," prompting the pretentious elder to engage her presumptive son-in-law in a form of interrogation intended to elicit personal information that illustrates Jack's qualifications for marriage to Lady Bracknell's daughter. Informed by Jack that he was found as a baby in a bag at a railway station, Lady Bracknell recoils from the suggestion that her daughter would marry someone of such lower-class origins:

"To be born, or at any rate bred, in a hand-bag, whether it had handles or not, seems to me to display a contempt for the ordinary decencies of family life that reminds one of the worst excesses of the French Revolution."

Up to this point, the question-and-answer session seemed to leave open the possibility that Jack, deficiencies aside, could be judged suitable material for Gwendolen. The information regarding his unknown parentage, however, has shut the door on that possibility. 

So, what prompts Lady Bracknell to change her mind about Jack/Ernest? Wilde's play is thoroughly improbable, as he knew full-well, but plausibility is hardly the point of The Importance of Being Earnest. Rather, it is the pretentiousness of England's upper-class society and its social rigidity that Wilde sought, successfully, to satirize. That is why, as the play enters its denouement, the highly unlikely revelations about Jack's life provide the opportunity for the happy ending the audience would expect. As Jack experiences the epiphany regarding his origins, he increasingly emerges as suitable material for Gwendolen's hand in marriage. As Lady Bracknell notes when confronted with the fact that Jack's origins are decidedly more upper- than lower-class, and that his parentage was that of the landed aristocracy, "Every luxury that money could buy, including christening, had been lavished on you by your fond and doting parents." The revelation that Jack comes from old money, if he never actually knew that, is enough to warrant his inclusion in the elitist atmosphere occupied by the Bracknells, and that is sufficient to make him suitable for marriage to Gwendolen.