Elevated, Masterly, Lucid, All-knowing, All-disapproving
The narrator of Ivan Ilych is "above" all that he describes. He conveys an air of knowing everything there is to be known in the story and of having complete control over its presentation. That's in large part because he's able to penetrate every character's mind. The narrator describes what's there, with total confidence and clarity, with no more language than he needs or excessive poetic waxing. It's as if he always remains outside of the characters but can focus at will on any one he wants to see. Look at this example, one of the most famous passages from Ivan Ilych:
Ivan Ilych saw that he was dying, and he was in continual despair.
In the depth of his heart he knew he was dying, but not only was he not accustomed to the thought, he simply did not and could not grasp it.
The syllogism he had learnt from Kiesewetter's Logic: "Caius is a man, men are mortal, therefore Caius is mortal," had always seemed to him correct as applied to Caius, but certainly not as applied to himself. That Caius – man in the abstract – was mortal, was perfectly correct, but he was not Caius, not an abstract man, but a creature quite, quite separate from all others. He had been little Vanya, with a mamma and a papa, with Mitya and Volodya, with the toys, a coachman and a nurse, afterwards with Katenka and will all the joys, griefs, and delights of childhood, boyhood, and youth. What did Caius know of the smell of that striped leather ball Vanya had been so fond of?... "Caius really was mortal, and it was right for him to die; but for me, little Vanya, Ivan Ilych, with all my thoughts and emotions, it's altogether a different matter. It cannot be that I ought to die. That would be too terrible."
Such was his feeling. (6.1-4)
With the first line, the narrator summarizes Ivan's general state of mind. With the second line, he reveals that he knows Ivan much better than Ivan knows himself. He sees to the "depth of his heart," to something Ivan himself is vaguely aware of but still can't understand. Then the narrator goes on to describe Ivan's own thought process, such that the reader can understand it and identify with it easily. The narrator even concludes in real-time by giving us Ivan's thoughts in direct first person. Then, he's back out with that summary "such was his feeling" line. Right to the depths of Ivan's soul and out again.
The narrator also appears to have total control over time and space, which affects how he comes across. At the extremes, he can stretch a few pages to cover thirty years and then contract the next few to cover five hours. In much of the book the narrator goes back and forth between describing habitual actions or states of mind (Ivan's visits to doctors; his overall feelings about himself) and then zooming in to particular episodes in real-time (a particular visit Ivan had with one doctor; a particular thought Ivan has). Even in that passage above, there's a lot of zooming in and zooming out. Since the narrator can do that, you get the feeling that every detail he gives you is for a reason.
Finally, the narrator adds to that all knowing air of his by saying things like "Peter Ivanovich, like everyone else on such occasions, entered feeling uncertain what he would have to do" (emphasis added; 1.24). The narrator doesn't just know Peter Ivanovich inside out; he knows how everyone acts. And he does that all the time.
So the narrator is the Master of the Universe, at least when it comes to Ivan Ilych. Not only that. He is using the story to make a point about the meaning of life. Why else would he give grand pronouncements like: "Ivan Ilych's life had been most simple and most ordinary and therefore most terrible" (2.1). That right there tells us matter-of-factly what the whole story will illustrate: Ivan Ilych lived wrongly.
One more thing. Doesn't it feel like the narrator disapproves of just about everything and everyone he describes? We're supposed to disapprove too; that's part of how he makes his point. But the thing is, he never comes out and says, "Aren't these people awful!" Instead, his tact is subtle. He just describe the characters and their actions with his characteristic clarity and leaves us to draw out the necessary conclusion. Let's look at one particular example:
Praskovya Fedorovna recognizing Peter Ivanovich, sighed, went close up to him, took his hand, and said: "I know you were a true friend to Ivan Ilych..." and looked at him awaiting some suitable response. And Peter Ivanovich knew that, just as it had been the right thing to cross himself in that room, so what he had to do here was to press her hand, sigh, and say, "Believe me..." So he did all this and as he did it felt that the desired result had been achieved: that both he and she were touched. (1.29)
Both characters come across as disgustingly fake in this passage, but all the narrator does is describe what Peter Ivanovich feels and what Praskovya Fedorovna appears to feel. It's hard not to detect a note of disgust in this, but if we look for signs of it in the words, there aren't any there. The narrator just described what the people thought and did, with that awful clarity of his. The effect? It seems as if he's just letting reality speak for itself, rather than coloring it himself. Since the narrator knows everything, he just happens to see reality as it is.
Doesn't that make the narrator sound an awful lot like God? He's not giving us his perspective, he's giving us the perspective. He's the one who knows reality as it is, through and through. In addition, he alone can separate the true from the false. It's not reality that's speaking for itself, but a world Tolstoy has imagined and designed meticulously to produce a particular effect in us, his readers. What's incredible is how convincing he is.