How do I explain the social conventions of the time through the character of Lady Bracknell?
Lady Bracknell is one of Wilde's more comical and colorful characters, truly representative of the Victorian values (or lack thereof) and their over preoccupation for superficiality.
In her, we see every convention of the time: The upper-class woman seeking to marry off her daughter Gwendolyn to a name and a last name, to property,and to money. This is evident in Act One where she grills Ernest asking him all kinds of questions about his income, properties, and assets. However, when Ernest explained to her that he had no parents he could be traced to, and that he was found in a handbag, his money meant no more for Lady Bracknell. Now, her problem was a very Victorian preoccupation: Rank. Lady Bracknell made no mystery of the fact that she could not possible marry her daughter to a "parcel". This shows the Victorian exaggerated need to stick a label to people in the form of rank, or title. It also shows how women needed to climb in society through marriage, and how marriage was not just love liaison, but a business transaction.
In Lady Bracknell we also see the how Victorians with title did not hide the fact that they thought of everyone else inferior. To this, add the hypocritical sense of morality she imposed in Gwendolyn whereas Bracknell's own family had scandal in their background after the "lost baby" scandal brought in by Miss Prism.
Another conventionalism involves keeping with appearances, keeping up with "the season" (London season of visiting and entertaining the likes of her), snobbery to those below in status (like the way she treated Ernest), and her overlooking of the issues going on in her own family circle, such as Algernon's obvious double life through Bunburying.
She is the embodiment of Victorian conventional thinking, their superficiality, tendency for hypocrisy and importance about the unimportant. Even her language reflects her shallowness. Yet, just like Algernon, you have got to love to hate them and hate to love them.