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The significance is the comic irony of these two guys claiming to be royalty. The two men are humbugs and frauds who were running away from townspeople who meant to tar and feather them. One man is about seventy and balding, and the other is in his thirties. The younger man specializes in printing and theater while the older man often "works" camp revivals.
The younger man then tells them that he is actually the direct descendent of the Duke of Bridgewater and therefore is a Duke. Both Huck and Jim start to treat him as royalty and cater to his every need. This makes the older man jealous and so he then tells them that he is the Dauphin, or Louis the XVII. Huck and Jim treat both men as aristocracy, although Huck comments that it is pretty obvious neither is true royalty.