A lot of people spend a lot of time and effort trying to explain to everyone what Anarchy -is-. But that can be difficult, given that everyone will always want to lay claim to the ability to define terms in a discourse. So rather than explain to everyone what it simply -is-, I will tell you what it is to -me-.
To me, Anarchy is a state of being. A hope for the future, both for myself, and for the rest of humanity, and perhaps, some future children I might have one day. A hope that both myself and others will be able to work and improve our lives without being stopped at every turn. To be able to simply work for -yourself-, without worrying about accomplishing everything that must be done to appease the people of the government, their taxes, their restrictions on what you may and may not peacefully do. Their arbitrary claim to own every piece of ground within their borders, denying so many people the ability to make a home for themselves on their own terms.
To me, Anarchy is Hope.