Confessional writing
In literature, confessional writing is a first-person style that is often presented as an ongoing diary or letters, distinguished by revelations of a person's heart and darker motivations.
Originally, the term derived from confession: the writer is not only autobiographically recounting his life, but confessing to his sins. Among the earliest examples is St Augustine's Confessions, perhaps the first autobiography of Western Europe. In it, he not only recounted the events of his life, he wrestled with their meaning and significiance, as in a passage where he tried to fathom why he had stolen pears with friends, not to eat but to throw away.
Jean-Jacques Rousseau turned it to a more secular purpose in his Confessions.
From this meaning evolved the meaning of writing that reveals more of the writer's heart and motivations, particularly the darker reactions, and the events that are normally kept secret.
Fictionally, the confessional story is a story written, in the first person, about emotionally fraught and morally charged situations in which a fictional character is caught. These stories may be anything from thinly veiled recountings of the writer's life, to completely fictional works.