In this play, the upper classes care about being respectable – so much so that they do a lot of lying about it. In general, Victorian upper-class society holds slightly different expectations of men and women. Men need to be upstanding, rich, and from a good family. Women need to be upstanding, rich, from a good family, and chaste. Any deviation from the rules (being born poor, or being found in a handbag, in Jack's case) may prevent a young person from making a good match, and continuing his noble line.
The ultimate goal in Earnest is to reconcile romantic desires and respectability; in other words, Jack, Algernon, Gwendolen, and Cecily all strive to make their less-than-honorable courtship look appropriate to Lady Bracknell.
Although each character in Earnest strives to be respectable, none actually believes in the socially-prescribed standards, and all often mock the idea that one can be both respectable and happy.