Note that this doesn't mean I believe in the absolute chaos and discord. Such stereotypes do not reflect what a majority of anarchists believe in. So what is Anarchism then? To put it simply, Anarchism is a political tendency with a long history, the core truth of which is that we all get along better–individually and collectively–if we keep the processes of social organization simple, local and responsive to new conditions and desires.
For a more elaborate answer designed for you sophisticated blokes here's Kropotkin's take on Anarchism:
ANARCHISM, the name given to a principle or theory of life and conduct under which society is conceived without government – harmony in such a society being obtained, not by submission to law, or by obedience to any authority, but by free agreements concluded between the various groups, territorial and professional, freely constituted for the sake of production and consumption, as also for the satisfaction of the infinite variety of needs and aspirations of a civilized being. In a society developed on these lines, the voluntary associations which already now begin to cover all the fields of human activity would take a still greater extension so as tosubstitute themselves for the state in all its functions. They would represent an interwoven network, composed of an infinite variety of groups and federations of all sizes and degrees, local, regional, national and international temporary or more or less permanent – for all possible purposes: production, consumption and exchange, communications, sanitary arrangements, education, mutual protection, defence of the territory, and so on; and, on the other side, for the satisfaction of an ever-increasing number of scientific, artistic, literary and sociable needs. Moreover, such a society would represent nothing immutable. On the contrary – as is seen in organic life at large – harmony would (it is contended) result from an ever-changing adjustment and readjustment of equilibrium between the multitudes of forces and influences, and this adjustment would be the easier to obtain as none of the forces would enjoy a special protection from the state.
That sounds alright, doesn’t it? We’re not talking about Eden here. A lot of conflict, and a constant labor for liberty, is tucked away in that phrase about “ever-changing adjustment and readjustment of equilibrium.” Reading Kropotkin it’s hard to imagine why folks so immediately back away from the very thought of anarchism. After all, the “no government system” ought simply to be the vanishing point–which is to say, the point of perfection–of any government truly of and by the people. And isn’t that what we’re fighting for?
To make this more clear for Americans, Anarchists are simply unterrified Jeffersonian Democrats. They believe that ‘the best government is that which governs least,’ and that which governs least is no government at all. The most flexible, simple, and local government is no government.
If you have more questions about anarchism make sure to reply or PM me. I'll be happy to answer.