from the World Book Encyclopedia dictionary:

An-ar-chy (anerki) 1. The absence of a system of government or law. 2. Disorder, confusion, lawlessness. 3. Anarchism syn: Chaos


From Dictionary.com
an·ar·chy ( P ) Pronunciation Key (nr-k)
n. pl. an·ar·chies
Absence of any form of political authority.
Political disorder and confusion.
Absence of any cohesive principle, such as a common standard or purpose.

The root of the word, anarchy:
From the Latin, which was taken from the greek anarkhos. An; Without. Arkhos; Ruler. An-Arkhos; Without ruler.


WordNet ® 2.0, © 2003 Princeton University
anarchy

n : a state of lawlessness and disorder (usually resulting from a failure of government) [syn: lawlessness]

A leading modern dictionary, Webster's Third International Dictionary, defines anarchism briefly but accurately as, "a political theory opposed to all forms of government and governmental restraint and advocating voluntary cooperation and free association of individuals and groups in order to satisfy their needs." Other dictionaries describe anarchism with similar definitions. The Britannica-Webster dictionary defines the word anarchism as, "a political theory that holds all government authority to be unnecessary and undesirable and advocates a society based on voluntary cooperation of individuals and groups." Shorter dictionaries, such as the New Webster Handy College Dictionary, define anarchism as, "the political doctrine that all governments should be abolished."

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now obviously you've decided to refuse to respect a short blurb on the system, so i'm gonna go a bit more indepth here and see if that will satiate your opinion of me as a person "attempt(ing) to make suppositions about it out of complete ignorance."

Anarchic theory, as political idea rather than a reality, which existed throughout a good portion of ancient history, was first set forth in Political Justice, a book by William Godwin in 1793. He was recognized for a bit, but overshadowed when Proudhon came along with "what is Property?" Which set the idea that property shoudl not be owned by the individual, but rather used peacefully by the collective masses. It also figured Key into the introduction of communist and socialist theory later on, obviously.
You're now going to end up with contemporary theorists; Bakunin, then Kropotkin, the tolstoy. Now everyone likes to scream Tolstoy and Chomsky on the subject of anarchy, but you need to go back to your roots to get to the essence of it.
Tolstoy was helpful in addressing a number of ideas, one of which was that idea of violence in an anarchic system. according to Tolstoy, Any Violence that occured in an anarchic system could not be greater than that which would be caused BY the current system. That's obviously debateable. I take the example of Charles Manson. Let say Charles Manson lived in an anarchic society. He goes around with his followers killing all these folk and people start to realize, Hey! theres a WHOLE lot of nasty looking murders about. Now explain to me, how they would catch and stop him? because he, while in an anarchic state, is not quite getting the "no infringment on my personal rights" thing. now, you can't institute a volunteer police force, because without authority to push past some peoples rights they can't investigate. obviously if they show up at someones house while manson's followers are killing them, they aren't going to be too keen on letting you in the house. what are the police to do? they are anarchist police, they can't infringe on their rights, that would make them *gasp* AUTHORITY! so, the police angle doesn't work. you're stuck with a bunch of scared citizens with no way to stop the madman. he can go around all he wants doing exactly what he wants because there's no authority to stop him, and the only way he COULD be stopped is if someone else decides to violate the treatise of Anarchy, and form some form of order imposed on the masses, thus elminating anarchy in that time and place.
Now, you've got that famous "Haymarket eight" murders in Chicago. This got word out alot in america, and spawned a whole number of different american anrachist philosophers and supporters. You've got Cleyre, Parson's, and Goldman following after that, Goldman in particular getting some new blood by way of Anarchist Feminism that she helped found. Paris Commune and Zappata in the Spanish Revolution in 1936.....
and together with a number of other major movements in recent history (the largest as far as teh media is concerned being the huge Punk movement in the 70's and 80's, though a number of Punk groupings favored either socialims or Communism as well) have brought anarchy to be one fo the biggest "rebel teen" philosophy's on earth.

Now then. I will repeat my argument and hopefully it will nto be cast aside due to my "ignorance" of the subject. In an anarchist system, consisting of NO ASSIGNED GOVERNMENTAL AUTHORITY, there would be no way to keep defectors in check. through use of violence of intimidation, Anarchy would be quickly eliminated as a state of existence, because roving gangs or terrorist groupings would be established as a new, and more devious government. They would be so, because within the citizens groupings, assuming anarchist philosophy is maintained, and collective group to combat them could never be formed becasue it would require the use of authority to function. Anarchist philosophy, in order to succeed, would require complete and total one-ness opf mind by the entire population of an area, a fact that will never come to be in large4 groupings. THUS, outside of a hippy commune growing carrots in west virginia, you will never see anarchy in action.

Man, it should not have taken that much effort to get a point across withoutbeing called "ignorant."