This is the basis of my system: "Laissez-faire, laissez-passer!" ... Thus I demand, for each and every member of human society, freedom of association according to inclination and of activity according to aptitude. In other words, the absolute right to choose the political surroundings in which to live, and to ask for nothing else. - P. E. de Puydt, Panarchy
Panarchy is basically the idea of competing governments. In de Puydt's original conception, people would register for the government of their choice, with a nominal administration fee for switching. The critical difference between this and the statist quo is that one need not move or emigrate to switch governments. Governments would co-exist and compete in the same geographic area, and new governments could start up anytime, so long as they could attract enough members to be feasible.
Before going on, we should point out that government in this sense in not a state. The word "government" can have two distinct meanings. Normally, people use the term to mean "state" - an effective monopoly on the legitimate/legal use of force in a particular geographic area. This is definitely not what de Puydt means. Another meaning of the word "government" is: an organization intended to provide security. This is the meaning of "government" when used, for example, by John Locke in his Two Treatises on Government, by Thomas Jefferson in the US Declaration of Independence, and most explicitly by Albert Jay Nock in Our Enemy the State.
This double meaning of "government" is the source of many fallacious equivocations in political writings, not to mention one major cause of the popular misunderstanding of anarchism. Many people not familiar with anarchist thought assume that anarchists are against law, or police, or property. In their limited experience and narrowness of thought, they see these human goods as intrinsically connected with state. In fact, anarchists are not against law; we are against monopoly law. Anarchists are not against peace officers, but against monopoly police force. We are not against property in its general sense, but against monopoly decreed property schemes.