Anarchy, as I've been defining it, is "self government". Not necessarily the absence of society, just an absence of putting some bureacrat in control. "Laws" are what everyone agrees on and every man is for himself with equal respect for every others individuals Right to the same.
Not this "no laws, no morals, no consequences" BS some of these people advocate. Scratch one of them too deep and you see commie Red.
Over the past couple of centuries "anarchist" has had a number of meanings. Typical anarchists in the late nineteenth century were leftists, and were often referred to as "bomb throwers," since that was a favorite method of protesting against the reactionary establishment.