http://www.ozarkia.net/bill/anarchism/faq.html
1. What is anarcho-capitalism?
Anarcho-capitalism is the political philosophy and theory which asserts that
1. the State is an unnecessary evil and should be abolished, and
2. a free-market private property economic system is morally permissible
Part one is simply the definition of "anarchism," and part two is soft propertarianism, known more generally as "a free market" or "laissez-faire." Let's look more closely at each of the two parts of our definition. Moral permissibility is a "minimum" position. Almost all anarcho-capitalists believe also that a laissez-faire economic system is generally better than alternatives. Some strong propertarians, such as objectivists, go further and claim that laissez-faire is the only moral economic system.
A typical dictionary definition[Onelook] of anarchism is:
"The theory or doctrine that all forms of government are oppressive and undesirable and should be abolished." - American Heritage Dictionary
This definition follows the etymology of the word: "Anarchism" is derived from the Greek αναρχία meaning "without archon" (ruler, chief, or king.) This is the core meaning of the term - against the State. This means against it in principle, as an institution, not merely against certain policies or personnel.
Murray Rothbard coined the term "anarcho-capitalist" in the winter of 1949 or 1950.
"My whole position was inconsistent ... there were only two logical possibilities: socialism, or anarchism. Since it was out of the question for me to become a socialist, I found myself pushed by the irresistible logic of the case, a private property anarchist, or, as I would later dub it, an anarcho-capitalist." - [Cf: MisesWiki: Rothbard]
Some prefer the term market anarchism to avoid the negative connotations associated with "capitalism," while others prefer private property anarchism or voluntaryism.