Many of the great commentaries for intellectual, modern-day anarcho-warriors have been written by Murray Rothbard, a man who unfortunately did not live to see the proliferation of the Internet and experience the enlightened online communities of autodidacts. One of the most thought-provoking 'Net age popular commentaries was written by Roderick Long - "Libertarian Anarchism: Responses to Ten Objections." Long's essay, a transcription of a long talk he gave at the Mises Institute, is not necessarily the most suitable read for the general reader who desires to satisfy a trivial curiosity about a concept that doesn't merit much of his time or thought. Long's splendid talk was geared toward advanced students, though using simple abstractions.
That said, this article from Cat Farmer, an oldie-but-goodie from the young and flourishing days of libertarian Internet presence, may be one of the most basic and clear expositions of anarchy in short form. Cat, rather than introducing pedantic concepts and philosophical or historical themes, speaks mainly to the notion of a spontaneous anarchical order that emerges when the coercive state is held to be immoral and, as Cat notes, there arises a "conscientious objection to the tyranny of other people's visions, opinions, schemes, fixations, and priorities." Here is a quote from Cat's essay:
Anarchism is not a utopian scheme, because if we're all able to create our own little interlocking utopias, then no two will be alike. There is no one-size-fits-all paradise, and one person's heaven may indeed be another's hell; to force your heaven upon someone else is as atrocious an act as creating a hell for him. Good intentions are no excuse for making prisoners and hostages of people who have less political clout than you do.Read the whole (short) article here: "What Anarchism Means to Me." This is how I picture a model for anarchy for a city like Detroit where the government is deemed insignificant by both libertarians and progressives, and in fact, the regime and all satellite authorities are considered to be a hindrance to humanity and community prosperity.