Early modern Christian Platonists argued that Plato essentially was a precursor to Christianity and such individuals pointed to a few particular passages to make their case. Many of these passages relate to what is call “Plato’s unwritten doctrines” or ideas that Plato did not write down but only taught orally.
Plato’s pupil, Aristotle, refers to Plato’s “so called unwritten doctrines” in his Physics. In Plato’s seventh letter, Plato says, “There is a true doctrine that confutes anyone who presumes to write anything whatever on such subjects” and that “anyone who is seriously studying high matters will be the last to write about them. Whenever we see a book … we can be sure that if the author is really serious, this book does not contain his best thoughts; they are stored away with his fairest possessions. And if he has committed these serious thoughts to writing, it is because men, not the gods, ‘have taken his wits away’” (Letter 7, 342a, 344c-d, quotes from the 1997 Hackett edition).
Many question the validity of all of Plato’s letters (letter 7 is viewed as the mostly likely to be authentic), but Plato says very similar things in the Phaedrus, one of his most important works. “When it has once been written down,” Socrates tells Phaedrus, “every discourse rolls about everywhere, reaching indiscriminately those with understanding no less than those who have no business with it, and it doesn’t know to whom it should speak and to whom it should not” (275e). Better is the “man who thinks that a written discourse on any subject can only be a great amusement, that no discourse worth serious attention has ever been written in verse or prose … that at their very best they can only serve as reminders to those who already know” (278a). The best way to “write” is “in the soul of the listener” (276a).
John Dillon, when looking at Plato’s intellectual legacy among his first followers argues that Plato did indeed have an oral tradition and that his dialogues “which, literary masterpieces though many of them are, were for Plato only ‘entertainments’—by no means devoid of substance, but certainly not straightforward presentation of his most serious speculation.” However, Dillon argues, bits and pieces of his followers’ philosophy hint at what Plato’s secret doctrine might have been.
I’m no expert on this esoteric and long debated topic, but in the posts that follow, I’m going to put up some musings on Plato’s secret teaching and some interesting similarities to Christianity, ones that Joseph Smith may have been aware of.
 John Dillon, The Heirs of Plato: A Study of the Old Academy (347-274 BC) (Oxford: Clarendon, 2003), 16-17.