I guess people like it because it is pretty good, and it's a fantasy story without the softness the genre usually carries. The characters are interesting and the story is strongly centered around politics rather than the usual fantasy adventure. My main criticism: as with most HBO series it has a much larger amount of PORN than it would be necessary, and I get it, people like it but wake up, it means you'll spend 20 minutes watching porn when they could be using this time to advance the story itself, instead of giving you another damn cliffhanger; sadly, nowadays they always find a way to consume show time with stupidity...
All in all, I enjoy Game of Thrones, I'm buying the show as they release it on Apple TV, BUT... Even though the story gives an impression of complexity, it is actually pretty shallow, and most characters (with a few exceptions) are more "cool and interesting" than actually deep and complex, as in, you'll hardly feel sad for somebody's death or really feel for someone else's love interested not working out.
I believe what calls the public the most is that it seems filled o the brim with those "jaw dropping tv show events" that somehow always trigger some inner instinct inside us even if we don't care about what happens, things like the massive and unexpected slap to the face a villain might get, or the impending raid to a given village filmed with some epic scale.
That's all based on the series, I didn't read any of the books, maybe I will someday but I don't think so, I'm too entertained by many other books and barely have time for them, including some classics I SHOULD have read by now (Dark Tower, Pratchet...); I know this is piss poor judgement, but the tv show is good enough for me but failed to be SO good as to convince me to go for the books, meaning "I'll enjoy the show instead of reading the book, it's faster"