According to Wikipedia (link included in title heading) cognitive dissonance is:
"...an uncomfortable feeling caused by holding two contradictory ideas simultaneously."
The article cited Aesop's "The Fox and the Grapes" as embodying the gist of this concept. For those who aren't familiar with the fable, a one sentence summary: A fox spies a bunch of grapes, fails to get at them as they are too high up, and concludes after three tries that the grapes probably aren't that tasty anyway. This is, according to social psychologists, one method people use for relieving cognitive dissonance--that is, amending their beliefs or opinions that are at odds with their respective environment so that they are no longer in conflict.
After a little digging around I came across an article I remember reading about in history class in high school:
The leader of a religious group known as the Millerites predicted that Jesus Christ would return on a certain day in 1844 (He did not, of course). Rather than rethink their choices to give away all their worldly possessions (a choice a good chunk out of the thousands thought it was a good idea to make) most Millerite faithfuls either came up with their own theories or accepted the explanations of their Millerite leaders as to why Christ didn't show up or would be showing up later. Consequently, a number of new sects emerged within the Adventist Church, each built upon a different explanation as to Christ's absence.