Tolstoy had A LOT to say and concise writing was not the dominant form of the time.
Well, okay, while I don't refute that those two reasons are pretty valid, I've been thinking about this question for some time and I'd like to offer another response.
When people ask me about War and Peace, the only somewhat suitable phrase I can come up with to describe War and Peace is "a slice of life." Tolstoy isn't telling us a 1200 page story or writing a purely philosophical discourse. What stands out about War and Peace to me from other books is that we, the readers, get to know the character's and their world similar to how we get to know people and our world in real life. To meaningfully accomplish that method of writing Tolstoy certainly needs 1200 pages. For many details in War and Peace you could argue that they are unimportant, which is in part a valid argument. If Tolstoy was writing in a style where he wished to explicitly describe each character and drive the story forward without "distraction," then I'm sure many details would be unnecessary. I think, however, that Tolstoy is attempting to draw us into the book slowly but surely by revealing characters to us the way we meet people in our own life. We get to know people around us simply by the sum of all their little actions and their conversations with us and those around them. That is how we begin to get to know characters in War and Peace; however, as we are accustomed to reading a different style of writing, we desperately want to know exactly how old the character's are, exactly where Pierre studied abroad, and what drives a character to act a certain way at a soiree. Much as in real life, we are left to just continue observing a character's actions and thoughts. One example that struck me is when Andrew has an epiphany, that something has changed in him is obvious, but we are not told what this epiphany is. This seems reflective of in real life when we can tell that something in someone has changed, but rarely would we be told in an all too explicit sentence what their "epiphany" was. While one could probably write a quite sufficient 15 page essay on Prince Andrew's character, the effect would not be the same as getting to know him the way we do in War and Peace. Those seemingly unimportant snippets of character's lives are important simply because of their "unimportance;" we get to know people by endlessly sifting through thousands of minute interactions.