A system of government (or lack there of) where everyone can do their own thing (that means ANYTHING) Anarchism is an idiots version of socialism, i.e. the state is the people and thereby serves the people by working for the common good, and halting those who do not (in most cases, corporations)-socialism. The funny thing about anarchism is, with no government to hold down greedy companies, anarchism becomes "corportate republicanism", (Sid Meyers, Civilization) whereby big business controls every aspect of life, from utilities and the military, to your paycheck and children's education, and the only democracy is between the leaders of major business around the globe. In essence, rather than bringin us towards a utopia, anarchism bring us closer to the ultimate exploitation of the human race.
Noun
1.} Horribly idealistic "state" where no figure leads the "nation." People are free to do as they wish, unfortunately people often choose to hurt others.
2.} Often adapted by teens wishing to be cool. Note especially the "pnk" genre of music.
"Aww, yeah, Billy! Ferget the Government, let's go be Anarchists because it is cool!"
A good idea, but will never work in practice. Unfortunately, people need to be told what to do, need to be controlled, need to have someone in charge to tell them "everything’s okay". People are just to comfortable. It's the fucked up way humans have evolved. Get used to it.