Anarchy is a theoretical form of self-government which is practically unattainable. Historically Anarchy only exists between the shifts between other known forms of government, and it is in fact no government. There are two types of Anarchists: punk rockers, and romantic political philosophers.
The main argument of anarchistic thought is that any appointed, hereditary, or aristocratic government is coersive in nature, and coersion is intrinsically evil. Therefore, all government is inherently evil. The only solution to eliminate coersion in society is to live in the state of anarchy.
The main flaw of this argument is that in order to completely eliminate coersion even in a system of direct democracy there cannot be majority rule, that is the whole society has to unanimously agree on all issues. This is not a practical solution, but a theoretical state of perfect unanimity which is an extreme condition only possible in theory, an utopia.
A state under Anarchy is either a state ruled completely and unanimously by all the people for the people, or a state in civil war.