Synopsis: aSoIaF (ugh, what an awful acronym) starts out revolving around the stories of the Stark family, eventually branching out to encompass other storylines as well. I really can't go into the details of the plot to much, because the spoilers start early on, but Lord Eddard Stark is chosen to become the king's Hand (basically an advisor + guy who manages everything) of the kingdom of Westeros. From there the plot explodes into a plethora of monsters, magic, spies, Machiavellian scheming, wars, betrayals, conspiracies, and other juicy stuff.
Review: This is a tough one to review. Everyone has likely either read these books already (perhaps multiple times) or watched the tv show, or at least heard everything from their friends. So it is a little tough to write a review with anything that hasn't been said before. That said I'll give it a shot.
George R.R. Martin (G.R.R.M. for brevity's sake) is a unique writer in the way he does things. I started Game of Thrones (GoT) loving it, got all the way through A Clash of Kings (aCoK) and A Storm of Swords (aSoS) still loving it, loved it a little less by A Feast For Crows (aFfC), and finally ready to read something else by A Dance With Dragons (aDwD), because 2000 pages of Westeros has proved to be a bit much for me. Not that I'm not still on board with this series, I just need a break for awhile.
The books are seemingly written to defy cliques wherever it can spot them. What you expect to happen doesn't happen, and characters you like or dislike will die; often abruptly when they do. Each book is only set on a very, very vague kind of arc, although they don't really seem to have their own flavors. GoT for example, is all about political scheming, and aCoK and aSoS are about the wars that follow this scheming, while aFfC and aDwD deal with the aftermath and cleanup of said wars. The plotline wanders up to and through all these arcs. It is extremely difficult to pin down where, if anywhere, it is going. The idea behind the plotlines seems to be that the journey is way more interesting than whatever the destination is. The one constant theme is that Westeros is brutal, unforgiving and treacherous.
The characters are a huge bright spot in this series. There are a wide variety of them, and your going to love some of them (and cry if and when they die), and hate others (and cheer when they go). There's a magnanimous lord with a difficult job to do, a good natured king who just wants to drink and party, a villainous noble scheming from the shadows, a brash knight with an ugly secret, a dwarf who compensates for his physical inabilities with intelligence and charisma (I drink and I know things), and a mentally challenged stableboy who can only say his name (HODOR). This is really only scratching the surface as G.R.R.M. has really tried to stuff the cast with memorable characters.
The most important takeaway from this review, however, is that aSoIaF is brutal. G.R.R.M. doesn't believe in censorship; there are sex scenes and graphic violence. He doesn't write to make things more palatable for his readers, instead he tries to model attitudes that might be common in a more primitive or medieval society. I'm the sort of person who enjoys this sort of open honesty, regardless of how I feel about the things described, but I understand how other people may not be onboard with it.
Summary: I loved these books, but I can see if they don't go well with other people. Most likely however, these books are on a track to be considered classics on par with Tolkien's Middle-earth.