As history, the book of course chronicles from the aristocratic Russian side Napoleon's invasion of Russia. Somewhat along the lines of Proust, part of the interest is the view we get of the aristocracy. And that view is of a bunch of idle useless pointless shallow folk. We occaisionally get to see the underside, of the serfs, but I think this is airbrushed, with the horrors removed out of sight. If you're interested in how the military campaign went, then read something else, because part of Tolstoy's art is to describe battles from a very detailed close-up viewpoint that emphasises how confusing they were.
And here we run inevitably into his theory of history. Oh yes, he has a theory. And he isn't subtle about it. I can't tell if he just lacks confidence, and so won't let the ideas speak for themselves as the book unfolds; or if he is perfectly well aware that what he describes doesn't demonstrate his ideas; but either way, there are chapters of theory, and even an entire epilogue of it. His brilliant theory, if you don't know it, is that the "Big Man" theory of history is wrong, and instead, that... well, his alternative is rather less clear. Either that history is made up of lots of little things, or that great movements of peoples from East to West <something>. I wasn't desperately interested, so find it somewhere else from someone who cares. For what it is worth. I think his theory fits the Russian side rather well: the Russians had no-one competent and their response - to keep losing until the French were exhausted - was what happened. But it doesn't fit the French side at all well.
As to the story apart from the campaign, well, it is the lives of various Russian aristocrats, and as a story it is all reasonably well told and moderately interesting. But I think he needed an editor.
I get the feeling that the book does represent something of how Russians view themselves and their people. Perhaps they think more now of the Great Patriotic War but either way it is living on past glories of times that weren't really glorious anyway.
Addendum: 2024/06: finishing Popper's The Poverty of Historicism, he briefly mentions Tolstoy, and agrees with his theory. I find that odd, since I don't think it fits the French side at all well; it is hard to see the Frogs bothering to invade Russia without Napoleon to drive them. But you may read his words here.