An epiphany is an experience of sudden and striking realization. Generally the word is used to describe a breakthrough or discovery. Typically this applies to an enlightened realization which allows a problem or situation to be understood from new and deeper perspective.
Epiphanies are relatively rare occurrences and generally follow a process of significant contemplation about a problem. Often an epiphany is triggered by a new key piece of information, but typically requires a depth of prior knowledge to allow the leap to understanding.
The Holistic Management process discussed on this blog a few weeks ago was a good example of an epiphany. Ten of thousands of African grazing animals were killed in a mistaken attempt to rest and heal the land. When it was determined that the exact opposite was needed.