Market economies are most often associated with capitalism. Capitalism is defined by the privatization of forces of supply and demand. The effects of supply and demand transfer capital from less desirable investments to investments that offer a more substantial return on the investment. Private property is a form of capital investment in one sense. A capitalist economic system differs from a Marxist or socialist economy on how capital is distributed and on private ownership of property. In a Marxist or socialist economy, in theory, there is no private ownership of property. Property is for the public good, and the use of the property or the distribution of property is government-controlled.
In a capitalist economic system, private property is considered an investment, and its use with some restrictions is controlled by individuals. Protecting property rights is one way of managing wealth. In countries where there is little or no protection for property rights, capital does not easily flow into the economy. If the idea is to maximize the return on investment for capital, no one is going to risk placing significant amounts of capital investment in countries where industries or private property can be confiscated and nationalized.
One example that underscores this point is Cuba. Before the revolution in Cuba, the country boasted a dynamic economy with capital flowing into Cuba from many parts of the world. After the Cuban Revolution of 1959 and the confiscation of private business (such as American owned oil refineries as well as other companies), private investment stopped. This eventually led to the nationalization of all private property, including property owned by native Cubans. The economy in Cuba today consists mostly of a handful of companies that are allowed to operate because they are affiliated with the current regime. Cuba is an example of why protecting property rights is essential to a market economy.
Don't be misled in thinking the United States has a perfect record for protecting property rights. For example, asset forfeiture and property seizure for drug arrests, suspected terrorist activities, and for some civil infractions have become too familiar of a practice that many civil libertarians are calling for national legislation to be enacted to protect people from the unwarranted seizure of assets.
Other examples are the expansion of eminent domain laws. Eminent domain laws allow the government to seize property that is deemed in the public good. If the government plans to build a road and your house stands in the way, under eminent domain laws, if a satisfactory agreement between you and the government can't be negotiated, in some cases property has been confiscated when it is deemed in the public interest. You will be compensated for the property, but the compensation may be far less than the investment and usage you have for the property.
Without the protection of property rights, a capitalist market economy would have little chance for survival. Protecting property rights has to balance with maintaining the public good. These two events inevitably conflict with each other. We then rely on the prudence of the legal system to settle claims of inequitable treatment of property rights.