In Lewis Carroll’s book Alice In Wonderland, Alice, a normal Victorian Era school girl, falls through a rabbit hole one day and finds herself in "Wonderland," an increasingly unreal world of talking animals, singing flowers, and litigious Queens.
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The original quote, "curiouser and curiouser" comes from this passage of the book:
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"’Curiouser and curiouser!’ Cried Alice (she was so much surprised, that for the moment she quite forgot how to speak good English). ’Now I’m opening out like the largest telescope that ever was! Good-bye, feet!’ (for when she looked down at her feet they seemed to be almost out of sight, they were getting so far off)." (Ch. 2)
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At this point, Alice has just eaten a cake (labeled "EAT ME") that has made her "telescope" up to 9 feet tall. As a proper (and fictional) young girl in Victorian England, her reaction to this is somewhat the muted exclamation, "Curiouser and curiouser."
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People will often use the phrase when they feel that they are seeing or experiencing something that does not make sense, or that imparts a sense of wonder. Sometimes the phrase is used in irony or with a sarcastic manner. I have, for example, been known to mutter "curiouser and curiouser" in staff meetings when it becomes clear that my boss is operating in a completely different level of reality than I am. Because of the -er on "curiouser" the phase also implies that one is being drawn further and further into some bizarre world or circumstance where one is merely an observer to the odd behavior of others.
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The Article on GOP.com titled "Curiouser and Curiouser," for example, discusses a disconnect perceived by the author between the Democratic Party’s rhetoric and its candidates’ actions. Using "Curiouser and curiouser" as the title allows the author to comment on s/he see as the increasing "bizarreness" of the DNP’s logic.
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As literary phrases often do, "curiouser and curiouser" has basically become literary shorthand for feeling of wonder and disbelief. It is widely used by writers to evoke those feelings.
