What is Anarchy?

The word “anarchy” is derived from the Greek words “an”, meaning without, and “archos”, meaning chief, leader or ruler. While I have read several philosophies of anarchism, I always like to refer back to the basic meaning.
Because of mass media propaganda throughout different societies, anarchy is often thought of as being synonymous with chaos. In nearly every interaction I have had with my comrades, it is quite the opposite of chaos; anarchist collectives are typically quite organized.