1. intended for instruction; instructiveIt's the third definition that causes the most diatribes regarding children's books, usually couched in some version of "What is the author trying to teach our children?"
2. inclined to teach or lecture others too much: a boring, didactic speaker (or story).
3. teaching or intending to teach a moral lesson.
The second one which causes said child to drop the book like the proverbial hot potato.
And the first that causes most authors to say "Lesson? What lesson! Where?"