What is the significance of the title The Importance of Being Earnest?

Oscar Wilde's wildly popular play The Importance of Being Earnest calls upon a long English theatrical tradition epitomized by William Shakespeare: the use of double and sometimes triple meanings. On one level, you may say that the characters are not "earnest" in their behaviors; that they are all frivolous and irresponsible. This would be on the satircal level; the level at which Wilde is poking fun at the ridiculaousness he sees in English society of his day.

On another level, each of the characters is precisely earnest in following their convictions. Cecily is adamantly earnest in having fallen in love with her guardian's rascally brother Earnest who lives and causes trouble in London. Gwendolyn is paramountly earnest in her conviction that she could never love anyone not named Earnest. Algernon is unjokingly earnest in and devoted to his need to be free to escape to the leisure of the country as a Bunburyist. John Worthing is wholeheartedly earnest in his ploy of escaping the tedium of the country by having an irresponsible brother named Earnest living in London who needs taking care of. Miss Prism...well...you get the picture.

Both Algernon and John adopt the name Earnest for rascally purposes that ironically gain them happiness and the loves of their dreams because both their loves have vowed never to marry anyone not named Earnest. So you can readily see how being Earnest would be extraordinarily important here. As it turns out, John Worthing is...or was...before he was put in the handbag...named Earnest, so for John, being Earnest takes on an added importance of birthright. 

The importance of being earnest has satirical meaning as Wilde laughs at English society for being so adamantly earnest about irrelevancies. It also has story meaning as the story is moved along by the various characters' earnestness in their, perhaps silly, convictions. It has plot importance because the conflict is in fact developed around the name Earnest and who will marry Earnest. It also has importance because the reverse-Bunburyism pulled by both John and Algernon adds witty humor and complications to the story. It is also important because the resolution of the play is in the discovery of John's true identity. Oh my. Being earnest/Earnest has rather a great deal of importance.