In Oscar Wilde's The Importance of Being Earnest, what makes the play funny?

What makes Wilde's play funny begins at line two of First
Act, scene one. Algernon is heard playing the piano from the room adjoining the opening
setting. He enters and asks his manservant, Lane, if he heard what was being played.
Lane responds: "I didn't think it polite to listen, sir." This is funny because Lane is
clearly being ludicrous: How could it be impolite to hear that which is very openly
presented, and how can one not hear piano music played without secretiveness in the next
room? In sum, Wilde throughout The Importance of Being Earnest has
his characters, one right after the other, say quite ludicrous things with perfectly
serious demeanor, as when Algernon later says:

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girls never marry the men they flirt with. ... It
accounts for the extraordinary number of bachelors that one sees all over the
place.

The next thing that
makes Wilde's play funny is represented in Algernon's rejoinder to Lane. Algernon says
that he regrets that Lane didn't hear because even though he does not "play
accurately--any one can play accurately," he does play with "wonderful
expression"--wonderful feeling and wonderful emotion. This is funny because Wilde takes
essential definitions of things--to play music is to play it accurately--and turns them
the other way round while the characters see the illogical things they utter as
perfectly logical. In sum, Wilde takes the assumptions of society and turns them into
inverted paradoxes that poke fun at presumption and artifice in society. This point is
further illustrated in a later exchange between Algernon and
Lane:

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Algernon.  [Languidly.]  I don’t know that I am
much interested in your family life, Lane.
Lane.  No, sir; it is not a very
interesting subject.  I never think of it myself.
Algernon.  Very natural, I
am sure.

The third thing that
makes this play so funny is the interplay between names and identities that is
introduced when Algernon says to Jack, who has recently come in and been directed to eat
bread and butter instead of extravagant cucumber sandwiches: "you will have to clear up
the whole question of Cecily."

The confusion of names and
and identities is a satire on society's insistence on marriage to a person with a good
name, which is a metonymy for having a good family background and lineage (metonymy: a
word closely associated with a thing, place, or concept that stands in for that thing,
place or concept, as in Washington for the U.S. government: e.g., It was decided in
Washington today ....). It is this confusion of names and identities that comprises the
bulk of the humor of the play, but the humor would attain lesser heights if not
bolstered by the first two elements of humor.