A market economy only works if people are free to do what they want (within reason) with their property. They are allowed to have money and are free to buy what they want. They are allowed to have property (like land or machinery) and use it how they will. This allows consumers to buy what they want and manufacturers to make what they think will sell. This is the basis of a market economy.
In addition, if people cannot be secure in their property, a market economy cannot develop. Who would spend money building a factory if the government might come and take it away from them? If people fear the government will not respect their property rights, they will not do the things that are needed to build a market economy.
A market economy is a system where prices and economic decisions are based on the forces of supply and demand. Government involvement in such systems is maintained at a minimum.
Private property and protection of property rights are important because it helps the economy deal with the issue of resource scarcity by ensuring its use is controlled through ownership. The private owner of a resource is expected to act in their self-interest to develop products and enhance profitability as provided by the forces of supply and demand. The individual would choose to use the resource or rent it out to the highest bidder. This results in a controlled competitive market where each participant is striving for increased satisfaction.
Private property and protection of property rights encourage investment because the owner enjoys a sense of security that enables increased focus on economic growth.