From what I've seen, there are two things to keep in mind about the story.
1) The story is bad. Blizzard's writers really dropped the ball with this, and there was a link posted earlier in the thread to what I thought was a spot-on analysis of a lot of what's wrong with it. The villains are neither smart nor threatening, the characters have no depth, and there's no mute button for the fucking companions who follow you around talking in circles.
2) Most of the actual story is told through optional conversations and book pickups. The cinematics and quest advancement conversations are shallow and all but meaningless, and if you want anything resembling a fleshed-out world, these are where you find the details. It's still not amazing - see point 1 - but it does make it a bit more immersive. Pretty much all of the plot to act 4 is in these, and act 3...well, act 3 you're trying to break a demonic siege, so I guess I can forgive a lack of meaningful plot advancement or character development.