Teresa Nielsen Hayden has the definitive post on the “Mary Sue” phenomenon: Mary Sue is an avatar of the author written into a piece of wish-fulfillment fan fiction. In a nutshell, the author interacting with their favourite characters — invariably swooning over or being swooned over by said characters. Not being a reader of fanfic, I’d never heard of this before — though this sounds vaguely familiar from some of the early Star Trek novelizations of the 1970s, especially the New Voyages anthologies. Hilarious to see The Left Hand of Darkness or Bujold’s Vorkosigan series (see comments) proposed as representative of the genre.