A personal essay is autobiographical and conversational in tone. Charles Lamb's "Dream-Children" arguably fits that definition.
In "Dream-Children," Lamb uses his persona Elia. He imagines Elia telling his children, John and Alice, about his childhood visits to his great-grandmother. He relates to them the great mansion his great-grandmother lived in and describes the fish pond there and the trees in the orchid. He also tells them of her death by cancer and of their uncle John's losing a limb, at which point they ask to hear about their late mother, Alice. But as Elia begins to tell them about Alice,
both the children gradually grew fainter to my view, receding, and still receding till nothing at last but two mournful features were seen in the uttermost distance
This sudden distancing occurs because Elia wakes up from his fantasy of having children and realizes that Alice married another man. Alice and John are not sitting at Elia's knee, for they do not exist. Elia returns to his own life and finds the "faithful" Bridget by his side.
The story is personal in that it is about the common but intimate experience of dreaming about other possible lives one might have lived. Elia misses his past—whether it be the precise past he describes to his "dream-children" or another past—but he also misses and feels a longing for the wife and children he never had.
This essay does not have the aims of standard essays. It gives no information; it does not instruct readers about, say, fishing or fashion. Nor does it seek to convey an argument on a debated topic. Instead, it relates what it is like to fall into a fantasy about a life different from one's own—a highly personal and private thing to do.