Metaphysical apartness means that the world of the movie (just as any fictional world, including those of novels, video games, or the like) is separated from the real world, it's 'apart' from it. Intuitively, the criterion for this is that we, the audience, are not in that fictional world, cannot be part of it — we're always outside it, merely observing. (Unless of course we are the author ourselves, in which case we're certainly not just observing, but creating the fictional world in question.) You can't walk or travel into a fictional world, have conversations with the characters in it, influence their actions and so on.
However, there are no limits to poetic license, and what you can't do in the real world, someone might just be able to do in a made-up world: imagine you are watching a movie in which an author writes a novel, and then steps directly into the novel she has written, perhaps with the help of some mysterious machine. Note that now we have three different worlds: the real world (in which you are watching the movie), the world of the movie, in which the author is writing and then entering her novel, and the world of that novel. Metaphysical apartness still holds between the real world and the world of the movie (it always holds between the real world and any fictional world). But there is no metaphysical apartness between the world of the movie and the fiction-within-fiction which is the world of the novel. Or, to put it differently, the law about metaphysical apartness is not in force in the world of the movie.
There is nothing overly surprising about that, of course. Just as you can think up a story which takes place in a universe in which the laws of physics are no longer in place (commonplace in science fiction of a certain sort), you can think up a story where the laws that govern fictionality are suspended. Remember, though, that this only works for fictional worlds and their fictions-in-fiction. It can't work for the relationship between reality and fiction, because the possibility to suspend laws that hold in reality itself can only arise in unreality.
In "Stranger than fiction", a writer (brillantly played by Emma Thompson) creates a fictional world in which the main character (also excellent: Will Ferrell) lives his life. In the beginning of the movie, we observe him going through a morning routine, while the author's voice describes it for us at the same time, thereby introducing the character. Thus far it's an unremarkable situation; it is common to have a voiceover narration in movies to get us into the story. It gets more interesting, however, when it turns out that the character himself can hear the narrator's voice. (A little later in the movie he describes it like this: "It's just a voice in my head. [...] It's telling me what I've already done... accurately, and with a better vocabulary.") This is where we realize that we're in a two-worlds situation (the world of the movie and the world of a novel that's written by one of the movie characters), and one in which the two worlds are not apart enough to prevent interaction between their inhabitants.
Strangely enough, all the impulses that cross the line between the two worlds come from within the inner-fiction world, i.e. from the world of the novel, the fiction-within-fiction. Since it is the world of the novel, however, we'd expect the author of that world to be omniscient (and controlling) of that world, and thus of all the thoughts and actions of its characters, too. In particular, shouldn't the author have known about the attempts of the main character to find her and prevent her from continuing and finishing the book? But she doesn't. (And of course, the movie would have been pretty boring if she had.)
The point here is not that the author should have known that the things she describes actually happen in her world (the world of the movie and the world of the novel overlapping each other to a significant degree); she finds that out empirically when she writes down the lines about the telephone ringing, and then hears the immediate effect when the telephone actually does ring. The point here, rather, is that insofar events happen in the novel-world, she'd have to know about them, and their motives. That's what seems not to be the case. There seems to be no clear and principled reason why she knows and controls some aspects of the fictional world she created and is ignorant about others. So presumably, there is a price to be paid, in the form of arbitrariness and inconsistency, for bending a law of fictionality.
 The term 'metaphysical apartness' is originally from Roger Scruton's Aesthetics of music, where it is used in a more narrow sense; I've discussed it a little in an earlier journal entry. Here, I use it in a somewhat different way, but I won't go into the reasons and motivations for that different usage at this point. I've also noted elsewhere a suspension of metaphysical apartness in Jasper Fforde's novels which is similar in some respects to the one discussed here in "Stranger than fiction".