It's a very vague and ambiguous term, but it's generally thought of as music that takes traditional "rock" instruments and aesthetics, but creates something that is completely unlike rock music as a whole, thus the term "post-rock". In a way, it's the natural
Evolution of rock music, mainly relying a lot on slow, minimalistic compositions (although GIAA does write shorter, poppier songs from time to time) and a bigger focus on atmosphere as opposed to melody for melody's sake. Sometimes it's hard to define what post-rock is and isn't in words, but it becomes very easy to spot after listening to the genre a bit. It's a very recent term- I read in an interview that only in the last few years has
God Is An Astronaut been called "post-rock" and before that they were just thought of as an ambient/electronica band.
I have a very love/hate relationship with the genre, since with post-rock there's a very fine line between sheer
Ethereal beauty and pretentious bullshit. Sigur Ros, Nyctalgia, GIAA and Do Make Say Think are all wonderful bands that bring me to the verge of tears, but Godspeed You! Black
Emperor and a couple others BORE me to tears.
If you are a false, don't entry, or you'll be burned and died!