I venture to say that true reading comprehension comes when you have sufficient knowledge of history, current events, politics, your own experiences...basically, when one can understand context. Not for all books, but for many of them.
The first book I read in this quest was Animal Farm, which is a satirical allegory of Soviet communism/totalitarianism. If I had read this book any time before, say, early 2006, I would not have understood it as well as I did last month. In elementary school, this book would been nothing to me except a bunch of talking animals on a farm. But beware, young knave; there is more to books than what is written on the pages. I knew little-to-nothing about systems of government. In middle school, I might perhaps have taken away the message to be suspicious of authority. In high school and college, I might have understood more of the message of the book.
However, only in last month's reading would I have "got" the message fairly in full. Why? My theory is because we are, for the most part, on our own now. I have more at stake in the matter (like taxes and providing for my family), so I pay more attention to government, economics, history, and current events, among other things. No doubt when I have more life experience 10 years later, I'll reread some of these books and say "I never would've understood the full message when I was 25."
How to get a youngling to truly comprehend the depth of what he's reading? I don't know. Foster an interest in the society in which they live, cultivate interest in history, ...stuff like that. To some extent, I suppose it's not possible for a child to comprehend on an adult's level. I imagine the maturity's not there, and even if you have an extremely precocious and mature child, there's the whole life experience and being-out-on-your-own factor. But what do I know? We have not been parents yet. I could be totally wrong on all this. (you will let me know, right?)
Now that I think about it, this post applies to any book that makes any sort of commentary on...well...anything. Hmm. That only means about...almost every book ever written. Good luck!
Of course, it's not only classics that benefit from a sufficient knowledge of context. For example, I am fond of some of Michael Crichton's novels. The first one I read was Jurassic Park, and that was in 6th grade. (what did I know back then?) I probably only took note of the parts where people were either 1) killing dinosaurs, 2) running away from dinosaurs, or 3) being eaten by dinosaurs. I reread it back in March and found it to be a much more enjoyable read, since now I had sufficient math/science knowledge to understand Ian Malcolm's ramblings about chaos theory and nonlinear systems.
What do you have to say about it? Any parents/adults that would like to add to the discussion?