This review contains no major spoilers for A Clash of Kings, but it does outline the basic premise of a few characters' storylines, and there are major spoilers for A Game of Thrones as well.
At the end of A Game of Thrones, a red comet appeared in the sky. Its presence dominates the opening chapters of A Clash of Kings, as every faction in the conflict rippling across the continent of Westeros interprets the comet as a portent of its own victory. At most one of these interpretations is correct, of course, and the book is silent on what the comet actually means, if it has any significance apart from the astronomical. That's the way of magic in this series; it's vague, difficult to explain, nothing if not equivocal.
Mysterious and strange though magic may be, its power is on the rise in A Clash of Kings. Whether, as is suggested at one point, its resurgence has to do with the birth of Daenerys Targaryen's dragons is another open question. What's certain is that magic casts its ominous shadow over the events of this novel, creating at intervals an atmosphere of uncanny threat uncommon in epic fantasy, more reminiscent of classic tales of horror, the supernatural, and the weird. The locations in which A Game of Thrones took place were largely based on medieval precedents, basically familiar to readers of epic fantasy, though reinvigorated by Martin's use of gritty historical detail. New settings in A Clash of Kings are less familiar, and more disturbing.
The book's gem of a prologue introduces readers to Stannis, brother of the late king Robert and a major player in the titular conflict. Stannis' home, the island fortress of Dragonstone, is a dark, eerie place, made all the more so by the arrival of a priestess from a distant religion. As an elderly adviser who raised Stannis after the death of his parents tries to curtail the priestess' rising influence, the reader learns of the sad history, grim architecture and melancholy inhabitants of the fortress. Full of world-building, character development, and hints of the impossible, this thirty-page chapter is a model of fantasy storytelling. Further chapters in this narrative strand, with a new point-of-view character, are less dazzling, but still excellent, and never without ambiguous aspects.
The second new point-of-view character introduces the reader to the Iron Islands, a harsh environment whose inhabitants live a harsh lifestyle not dissimilar to that of the Vikings. The bare, stony, sea-swept islands have their own religion, less comforting than that of the mainland; almost Lovecraftian, in fact. And then there's the city visited by Daenerys, an ornate mecca full of vast buildings, strange beasts, and warlocks. These chapters have about them something of Jack Vance, whom George R. R. Martin regards as the greatest living fantasist. Unlike some writers of epic fantasy, whose influences begin and end with Tolkien, Martin has read widely in fantasy, science fiction, and horror, and the vast world he creates reflects all of that reading.
But these new characters and situations are balanced by old ones, by the same mix of courtly intrigue and violent action that characterized A Game of Thrones. As the book opens, Tyrion Lannister arrives in King's Landing to act in his father's place as Hand of the King. But enemies and potential enemies are everywhere, from the eunuch spymaster Varys to the calculating treasurer Littlefinger to his own sister, Queen Regent Cersei, and her spoiled, unstable son, King Joffrey. Tyrion will need his sharp wit to survive, and indeed, he puts it to good use in some of the most entertaining chapters in the entire series. Although many of the protagonists of A Song of Ice and Fire fancy themselves to be master manipulators, Tyrion is the only point-of-view character who has a real genius for such things, and his fierce sense of humor lends his arc a particular edge.
Meanwhile, Arya Stark, daughter of the executed Eddard, is in disguise as a boy, being led north toward home. That course takes her through the lands devastated by the conflict the nobles of various houses have so blithely started, and gives her a rapid education in the cruelties of war. Death and disease are rampant, and only strength, intelligence, and bloody-minded cruelty of one's own offer a chance of survival. Despite being a young girl, Arya quickly demonstrates her growing mastery of all three. Like many characters in the series, she's on a dark road, and things seem likely to get much worse before they get better.
These are only some of the protagonists and situations of the novel, and I've barely hinted at the growing moral ambiguity of the series, created by the widening range of point-of-view characters, each with his or her own plans, flaws, histories, and justifications. A Song of Ice and Fire is truly a mammoth story, combining the best of epic fantasy, historical fiction, sword-and-sorcery, and horror. The author has described his childhood reading as "all sorts of weird stuff," and that's also a good description for this series: all sorts of weird, wonderful stuff.