When I explain anarcho-capitalism to the average person, I usually say that it is a philosophy that combines the peaceful society advocated by libertarianism with the rapid technological progress and high standard of living produced by capitalism.
Saying that anarcho -capitalism produces the most peaceful world, the best technology, and the most wealth is true. However, those are really just the effects of anarcho-capitalism. They are a kind of a hook to show how appealing ancapistan would be, but they do not really explain what it is.
To dig deeper, we need to define two things: freedom and liberty. First, freedom is
the absence of constraint. In other words, it is the ability to do what you want. Liberty is freedom from constraint by others, so it is a specific kind of freedom. Constraint by others is usually called crime or conflict.
Anarcho-capitalism has a value judgment that freedom is good. Life would be best if you could do whatever you want, i.e., if you had total freedom. That is not possible, so how do we make progress in that direction?
The first thing to do is get as wealthy as possible. The more stuff you have, the more things you can do. Food to eat, cars to drive, etc. Every bit of capital accumulation directly increases freedom. The laws of nature constrain us, but technology overcomes those constraints.
The second thing to do is to eliminate crime. Crime reduces freedom by reducing wealth, directly limiting what you can do, etc. So maximizing freedom necessitates defending liberty. Crime is the opposite of liberty, so every institution we make that prevents crime, or every criminal institution that we can get rid of, increases freedom.
It just so happens that the best solution to both of these things is the same. What is it? The non-aggression principle. The more people follow the NAP then, by definition, the less crime there is. To the extent that the non-aggression principle is enforced, people tend to cooperate, save, and accumulate capital. Both of these together maximize freedom.
You could theoretically get more personal freedom in the short run by stealing and committing other crimes, but you’re not one of the bad guys.
So in short, anarcho-capitalism is the freedom maximizing philosophy. It isn’t really a combination of libertarianism and capitalism. Libertarianism and capitalism are actually the same thing. One focuses on the liberty side of things and one focuses on the capital side. Anarcho-capitalists are the lucky few who see the whole picture.