an•archos: (Latin) no masters
For anyone who is curious about anarchy and what it is, you must rid youselves of any preconceived ideas or anything you may have heard and come at it with a new outlook. Many have used it to imply chaos, and if you believe that humanity needs an authority figure (be it a leader, president, prime minister, legislative body) to keep it from falling into chaos, then yes, no leaders would be chaos. However, if you do not believe in the legitimacy of anyone ruling over anyone else, than any leader would be tyranny.
Anarchy, today, has taken on many different shapes, such as the for-image title taken on by many within the punk scene or the libertarian-socialist perspective which is more a true political philosophy, since that is what anarchy truly is: a political philosophy. However, it is simply that, a philosophy, and not an answer, but we can also agree with Chomsky in that we do not know what would work and what would not, so it is also too early on to discredit it. What anarchy implies, basically, is no government and no rulers. It is utopian in the idea that people will coexist relatively peacefully and settle all disputes themselves as well as helping out their fellow humans. Because of the idea of no masters, it also has an inherent belief that their can be no private property. Property is a common, public good, and therefore, should not and can not be truly owned, bought, or sold. We can use it to our advantage and place our houses upon it, but to own land, something which one has not created, is sacrilegious.
Within true anarchy, there is also an idea of non-violence; violence being a rule/ruler imposed upon someone else. It is upon these basic tenants that anarchy is built and if you want more, research the various books on the subject, they are, for the most part, very good.