To fully grasp what's going on at this point in the book, we have to think of the significance of the Deathly Hallows, which are after all what the book is all about. The theme of the book is established many chapters earlier, at Godric's Hollow, with the twin New Testament passages, "The last enemy to be destroyed is death" and "Where your treasure is, there your heart will be also." Harry wants to destroy the power of death, to become the master of death, but the way in which he does so is crucial. It matters where his treasure is, what it is that he truly values. If he wants to overcome death for himself, to set himself up as its master, then he will be little better than Voldemort. This is the symbolism of the choice between Hallows and Horcruxes, which is built up throughout the earlier chapters of the book and comes to a razor-sharp point at Shell Cottage. Harry recognizes that he must choose between pursuing the Hallows, overcoming the power of death by taking to himself more power than death, or by embracing the route of powerlessness, the long hard path of destroying the Horcruxes, which means eventually giving himself up to death on behalf of others. (This fascinating dialectic is almost completely left out in the film The Deathly Hallows Part One, and so its resonances are absent at the crucial moment in Part Two, and the extensive conversation on this point between Harry and Dumbledore at King's Cross is omitted.)
Harry is to become the master of death, but master not by setting himself over it but by putting himself under it. Death exhausts its force by being poured out on him, the one who willingly seeks it for himself to save others. Love is stronger than death. "But I should have died--I didn't defend myself! I meant to let him kill me!" Harry exclaims. "And that," Dumbledore replies, "will, I think, have made all the difference." This enigmatic comment is left unexplained, but for the reader looking for an explanation within the existing logic of the books, Harry's cheating of death is explained in terms of the power of Harry's blood, itself clearly rich with theological overtones. The power of love in his mother's sacrifice is in his blood, and although Voldemort took Harry's blood to weaken Harry and strengthen himself, in this blood is the power of life that makes it impossible for Voldemort to finally kill Harry.
In short, in Harry's death, we witness the death of death in his own death. Like Christ, "death has no more dominion over him." What this means is more than just the destruction of another Horcrux; Harry has not just struck one more blow, but in fact the decisive blow. But to bring this decisive blow to completion, Harry must be resurrected. Death must be publicly exhibited as overthrown, its powerlessness before the power of love must be displayed and enacted, Harry must tread the powers of evil underfoot, must reverse the sentence of death that Voldemort has enacted on him by returning it upon Voldemort. And this resurrection must be no mere "rescuscitation," it must be the return to life of someone over whom death no longer has hold (more on this in the next section).
All of this, I think, is clear enough in the book, although generally hinted at rather than openly set forth.
In the film? Nope. In the film, the conversation between Dumbledore and Harry is abbreviated so as to omit any sustained reflection on the significance of what has happened, and Harry simply asks, more or less, "So, can I go back?" To which Dumbledore replies, more or less, "Well, if you want to." Why should he be able to go back? On what basis? Can the story just conveniently break the rules of its own world whenever it wants to? No, as in Narnia, what we have here is not the normal rules of magic, but a deeper magic at work. Thus far, the departure in the film is primarily one of omission, not commission, but the ramifications are still significant. The following features will show, I think, that I am not reading too much into this omission.
It's a long article, that's maybe a quarter of it. But it reminded me of why the ending of the book made me weep and feel full for days and why the movie made me feel, uh, yeah, that was pretty sweet.