An epiphany is an event where in a flash a person realizes the truth of a situation or when something that made no sense or that was thought to have no significance is suddenly understood all at once. 

The Epiphany described in the New Testament was the moment that Mary and Joseph realized that Jesus was quite unique, and was called to do something special when he visited the Temple as a small boy, and participated in the disputations that learned men were having there, and stayed in Jerusalem at the temple even when his party was returning home. 

James Joyce especially generalized this specific event reported in the Bible to other events that were interesting to a  storyteller or novelist. See this [article on epiphanies in Joyce and Wordsworth's work](http://www.mrbauld.com/epiphany.html).

If you hear someone using this phrase in conversation they likely have literary or critical training. Qualifying it as a "first-person epiphany" is evidence of this particular writer's cleverness. This whole phrase is not common usage. 

If you used it, you would have to likely have to explain that you mean a flash realization that a person has about his own situation or predicament. 

Might be OK to use epiphany in the vicinity of a University or among friends who were writers, English students or divinity school atendees. Could get you heckled or worse at a sports bar.