I'll be referring to events that have happened in book 1, A Game of Thrones, and book 2, A Clash of Kings, so you might want to skip this post if you don't want to read any spoilers.
So, instead of opening A Storm of Swords with Jon (captured by wildings), Arya (just having escaped Harrenhal and that pack of homicidal nutters, the Bloody Mummers), Sansa (stuck in King's Landing), Catelyn (who just let Jaime escape Riverrun with Brienne the Beauty and some Lannister), Daenerys (sailing from Qarth after torching some freaky magicians/sorcerers), or even Bran (escaping the ruins of Winterfell with Rickon, Osha, and the kids from Deepwood Motte), we open on a Prologue narrated by a very, very put-upon Brother of the Night's Watch and then get our first real chapter narrated by...Jaime? The arrogant sister-loving Kingslayer gets his own POV chapters now? Odd....
This is helpful, actually. Through Jaime we learn more about Aerys the Mad King and some of Jaime's true motivation behind his act of assassination. We also learn a little more about why Lannisters act the way they do - which doesn't make him endearing, it just clears the air. Jaime also develops a sudden weight-loss in the book which makes him a much more sympathetic character and he stops being a arrogant prick. Some of the time.
Daenerys is, well, still the Mother of Dragons and off in Essos. Her dragons are a little bigger but instead of heading for Westeros to take back the Iron Throne she somehow progresses to a one-woman abolishionist movement, crushing the cities of Astapor and Mereen (once she's bought and freed some many thousand Unsullied to fight for her - that was a clever trick). A character we haven't seen since the beginning of ACoK pops back up and that gets pretty interesting.
Sansa really starts to develop in this book and you really feel sorry for her. She has no one to trust and she's forced to marry Tyrion. We know Tyrion isn't a bad guy (out of all the Lannisters, he's probably the most decent, well, except for Kevan but we don't get his POV), since we get to read his chapters, but Sansa sees him only as a Lannister. Those times when she ought to confess the truth of what she's feeling to him all she sees is Lannister crimson and can't trust him. But she goes on an adventure at the very end - I would love to have a POV chapter for Petyr Baelish. That man is crafty.
We catch back up with Davos (who I quite like), Arya's storyline seems unclear, and Sam gets his own POV chapters (poor guy but he has a good heart) but it's Catelyn's last chapter that really sets the tone for what I think will be the remainder of the series. The Red Wedding sequence proves that no one in this epic has any integrity (except maybe Davos and Jon, we will see).
*Audio by Roy Dotrice, too - excellent, and we get to hear his Walder Frey voice again.