i think i would say that there are two components to "state"ness.
one is (as fba delineates) a body of people who, simply put, have a monopoly on violence (with the accoutrements that go along with that -- history creation, social structuring, etc). this deserves to be fleshed out more than i'm going to do right now...
the other is a more philosophical/psychological construct, one that permeates all/most of us, that has us looking to other people to frame questions for us, to structure reality (i had a more elegant way to say this when i started typing, but eloquence is fleeting... sigh).
but it's worth saying that the state is not just something divorced from you and me, it is not just an external force.
edit: this internal state-process is one idea that tries to explain (or at least address) the question of why people put up with things that seem so obviously terrible... ie, if we (anarchists) are not crazy, and things really are as bad as they seem to some of us, then how did people let things get this bad, and why don't more people rebel? perhaps it is something inside us that wants to be told what to do, that would rather not take responsibility for ourselves, etc.