OK, I've now read the first two books in the Song of Ice and Fire series, and I'm waiting on the 3rd volume to arrive at my local bookstore (in 2 parts here).
Bloody fantastic, real characters, flawed, selfish heroes and villans, but I think that I have nailed down WHY it's so believable, for a fantasy series it has a tiny proportion of fantasy elements,\
Spoilers
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The Others, mentioned as legend, appear briefly once, no explanation of the threat that they represent.
Re-animated corpses, happens once on the Wall, is mentioned by the 'free people' occasionally.
Dany's three dragons, seems to be a growing plot thread, but hardly driving the story, so far.
Bran's telepathic ability with his wolf.
Stannis's Red Priestess creating the shadow assassins, used to drive major plot pivots (the joining of the Stannis/Renly southern forces, the end of the Storm's End Siege to generate a big threat to King's landing so Tywin can come save them.)
I guess my point is that the human characters and their attributes drive the story forward, not gods, dragons, or other fantasy elements. I think that's what makes it so engrossing.