There are two parts to what states do: things that any individual can do, and things that only the state can do. Anarchy is just the limit of the observation that if one person doesn't have the right to do something, then two do not either.
Of course, this sidesteps a lot of questions, particularly about what "the right to do something" means and where it comes from.
In spite of the fact that Raymond is a hacker, I'm not sure that Hacker News is an appropriate venue for this discussion, though. :)
Personally I think ditching a couple hundred years of (largely arbitrary) legislation, not to mention taxation, is pretty appealing. Admittedly not everyone in our society is mature enough to cope with a world where nobody's "in charge" and there are some fairly thorny issues surrounding stuff like infrastructure and personal security but several sound proposals (on paper anyway) to deal with these complications have been put forward over the years.
Additional light reading on the subject: http://en.wikipedia.org/wiki/Anarchism http://www.infoshop.org/page/AnAnarchistFAQ
I don't believe you can have any form of "anarchy" (or any other social system) where people do not struggle to form a hierarchy, because that's what it means to be human, for better or worse.
I can't speak for the author, but the general idea is that because anarchy ("no rule") precludes the monopoly on violence that exists in state systems, there is better hope of some force countervailing the worst paroxysms of the majority. Think an extreme form of checks and balances.