A play on the word epiphany. When something occurs or is said that "clicks" with you to the point you have an epiphany.
Jane: "Ever notice that the biggest Christian holidays, Christmas and Easter, fall on the biggest Pagan holidays, conveniently?"
Jill: "OMG I just had a clickpiphany that the Christianity I was steeped in growing up could be bullshit. I now deem myself agnostic."