You've seen the cartoons in which characters say one thing—but they're thinking another. Authorial intention is sort of like that.
Contemporary literary theory pretty much debunks the idea that authors say exactly what they mean—because the words on the page don't always support their intended meaning. Or readers find additional meanings that authors hadn't considered.
Here's an interview with Peter Carey*, author of Parrot and Olivier in America and Oscar and Lucinda. An audience member asked Carey about an espisode in the latter novel that reminded her of Adam tasting the FORBIDDEN FRUIT.
Here’s Carey’s response:
Your way of reading holds up perfectly, I think, and it’s totally consistent with the book and consistent with my intention, and yet it never occured to me.
Then he said …
So isn’ t that the extraordinary thing about literature? It only really works when the reader reads it because until then…it’s words on a page…. Everybody brings their own lives, and their own experience, their own intellect… and then a book is made! And that’s the wonder of literature.
No one could have put it better. You can listen to the full interview from this 2003 BBC World Book Club broadcast.
* Carey, by the way, is a double MAN-BOOKER Prize winner. Yes, he won two times—for Oscar and Lucinda (1988) and for True History of the Kelly Gang (2000). (J.M. Coetzee and Hilary Mantel are the only others to win twice.)