Here's my stab at it. Spoilers obviously.
A Game of Thrones introduces us to the slowly brewing conflict between the great houses over control of Westeros. For about the first half of the book it is all political intrigue with occasional flashes of violence, which slowly turns into a full on war later in the book, leading to...
A Clash of Kings which chronicles the beginning of the War of the Five Kings.
The war reaches it's most violent peak in A Storm of Swords, and climaxes as House Lannister wipes the board clean of its competitors, declaring themselves the winner in all but name. But before the Lions can celebrate their victory tragedy strikes them as well.
A Feast for Crows, just like the eponymous birds of carrion, deals with the aftermath of the War of the Five Kings. All the major participants in the war are bloodied and exhausted, even the Lannisters who are the nominal victors, and the other houses start to nibble at the corpses to gather political power of their own.
A Dance with Dragons, which mostly runs parallel to AFFC deals with the dragon rider clan themselves: the Targaryens. Daenerys is fervently trying to consolidate her power, all the while her dragons threaten to become too big for their britches. Unbeknownst to her, many Westerosi are seeking her and not to assassinate her as per usual. Also, a man claiming to be Aegon VI lands in Westeros and starts carving a new Targaryen kingdom.