Where Are All These People Going (And Where Did They Come From?)

"Where do your characters come from?" A question I'm often asked, and a question for which I have no real reply. I've been writing fiction for many years, and yet I can't begin to explain how my characters are "born" or how they "grow." I've been asked to teach classes on characterization--but I can't. After all, how would you react to an instructor who walked into a room and announced that she had no logical explanation for the subject on which she was invited to teach?