Archibald's special skills are imitating a hen laying an egg and assimilating vast amounts of information in a very short period of time, as shown by his extensive reading of Shakespeare and Bacon in the space of a fortnight.
However, Archibald intends to display only one of these special skills, as he wants to convince Aurelia that he's a very intelligent, sophisticated kind of chap. So out goes the hen impersonation.
Instead, he's going to read as much as he can about Shakespeare and Bacon in an attempt to converse with Aurelia's dotty aunt, who believes in the ludicrous conspiracy theory that the great English philosopher Sir Francis Bacon was the real author of Shakespeare's plays. He hopes that this will impress Aurelia.
In the event, it turns out that Archibald got the wrong idea about Aurelia. Instead of being uptight and sophisticated, she's actually good-humored and down-to-earth, someone that really would like to see Archibald's legendary impersonation of a hen laying an egg.
Once he finds this out, Archibald is more than happy to show Aurelia his special skill, which she finds utterly delightful.