Anarcho-capitalism is the political philosophy and theory that:
The first is simply the definition of "anarchism," and the second 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 of anarchism is: "The theory or doctrine that all forms of government are oppressive and undesirable and should be abolished." 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."
Some prefer the term "market anarchism" to avoid the negative connotations some people have with "capitalism."