Here's the game in a nutshell: It can be played like a typical D&D game, where you adventure around the lands of George R.R. Martin's Seven Kingdoms, defeating robbers, wenching at taverns, etc—but that's not really what the game was designed for.
Rather, the quintessential ASOIAF game is one that mimics the progression of Martin's voluminous book series of the same name: the players create a noble house complete with a coat of arms, a house motto and a physical castle somewhere within the Seven Kingdoms. This house gets a character sheet all its own, detailing defences, land holdings, population, geography, natural resources and more. None of these factors are very high, because the game assumes you're playing a "starting" house that's just begun to ascend in terms of influence in the kingdom.
Only when the noble house has been completed does the actual character creation begin. Players generally make characters based on specific roles in the great house: the lord's son and heir, the hard-bitten tracker, the master of the castle's hound kennels, the brash knight, the shieldmaiden, etc. Crunch-wise, the characters are your typical modern fantasy archetypes, with skills and specializations and feat-like capabilities. I was never a min/maxer, so this segment of the game is lost on me—I just speed through it so I can get to the actual playing.
In ASOIAF, the characters' house is just as important as any other character. It is its own character. Everything the players do—defeating armies in the field or scheming in the royal court—has mechanical effects on the house and its stats. Characters can choose to invest their XP and their riches into their house, granting tangible improvements to various values, or they can keep their rewards and use them to improve their individual characters.
Moreover, since the characters are all integral players in their house, they call upon the house's resources at any time—but they should do so wisely, lest they squander them. In the game I played at my local game store, we were asked to head north and sort out a squabble between three minor estates. If this had been a typical game, we would have gathered our longswords and bows, mounted up on our horses and set off. Since it was ASOIAF, we mustered several hundred foot troops and some mounted knights and marched north en force. When we encountered raiders, we used the game's straightforward mass battle system to deal with the whole combat in maybe 30 minutes flat.
The game has a "social combat" system called Intrigues that is very similar in spirit to Burning Wheel. Characters can use social maneuvers to duel with friends and foes, hoping to gain the (verbal) upper hand and thus win the encounter. It's a bit crunchy for me, but I'm glad it's there, as you can really make characters to excel at this sort of play.
All of this works together to make the game feel very epic. I mean, I can say stuff like "OK, my character wants to scout ahead. I'll take 20 hand-picked horsemen with me" or "Well, I can't pay that retainer fee right now, but how about I offer to marry my house's firstborn daughter to your lord's heir?" I mean, that stuff is straight out of the books!
Here's the post-game writeup I posted on the game store's forum. I daresay it sounds like an excerpt from the books!
Anders Estermont, the third son of the Lord of Estermont, arrived at House Blacksun to deliver a request from his father, who rules from Greenstone Castle off the eastern shore of the stormlands. Three banner houses had fallen to squabbling with each other, and Lord Estermont beseeched the Bastard of Blacksun and his retinue to march north and set the matter to rights. Anders, for his part, was delivered as a ward to House Blacksun in an effort to forge a lasting friendship between the two houses.
Kerrick Sand, Ser Alric, Maester Dorian and Anders Estermont gathered the greater part of their infantry and horsemen and set off, marching overland for several days. They encountered evidence of wilding raids: burning farms, scattered lifestock and slaughtered smallfolk. They eventually arrived at a small town and met with Lord Tarbor (sp?), who commands the lands and owes fealty to a larger house to the north. After an attempted poisoning and a wildling ambush in the forest, the party figured out that Lord Tarbor's liege lord was dead, and that his sister had rallied the region's smallfolk in a bid to seize power. Even now she plotted her brother's downfall, no doubt, from some squallid hovel deep in the woodlands. Tarbor, however, was little better; he ruled with an iron fist and routinely terrorized his own serfs to ensure their loyalty.
Faced with the potential of a localized peasant uprising, the House Blacksun contingent mustered their resources and weighed their options carefully....
So all in all, it was a good start to the game. And it was very fun to actually roleplay alongside the storied characters and locations from Martin's books. The GM isn't as familiar with the source material as the players, so I forsee that becoming a problem at some point in the future as we increase our influence. But for now it's a fun counterpoint to the much more plodding progress of traditional RPGs.