Explanation
The play abounds with humour. The most serious matters are dealt with humourously and the mannerisms of some of the characters exude humour.
First we see Algernon eating up the cucumber sandwiches he has prepared for his aunt; his denial creates humour. It might have been a serious situation, perhaps, had it ben a matter between aunt and nephew alone. But Lady Bracknell's question elicits a lie from the master of the house, and this untruth is humorously supported by the servant, such that the audience wonders whether it has not been rehearsed. There is also the lineage of Jack which is another source of humour. Lady Bracknell's interview is, in itselt humorous. But the purpose and method are even more so.
Among many other things she suggests to Jack in her interview, she asks Jack to "acquire some relations as soon as possible". How he is to do this and "produce at any rate one parent... before the season is quite over" is ridiculously funny.
The quarrel between Gwendolen and Cecily is funny. especially when we remember Algemon's comment that two women meeting for the first time must quarrel to get on. As we watch Cecily carefully ask what Gwendolen will have, and offer her her dislikes, we find the country girl matching the city girl boot for boot. Lady Bracknell's surprise when Dr Chausuble asks Jack and Algernon whether they are ready for the christening is an occasion for humour. Apparently her ladyship is under the impression that the unborn child of her daughter and Jack is the object of the christening.
Jack's anger with Algernon leads to revelations that are complicated and funny. With Lady Bracknell determined to defend her nephew's honour, Jack is raging that Algernon has "obtained admission" to the house by pretending to be his brother. But Algernon is Jack's brother, anyway.