Adam Smith popularized the idea of the 'invisible hand' that guides market forces. The idea is that the demand of individual and groups of consumers when matched with the supply of the goods that are demanded will create a fixed price which will distribute all the goods (supply) to all the consumers who can afford it (demand).
Adam Smith did say that government intervention may be needed to balance the market forces. i.e. a large business can force out a small business, or find a way to cheat or scam consumers etc. (will be explaining this more in 'perfect competition' next)
The following are some extracts to help explain what a market economy is, then I will be getting into some of the basics of economics...
What Does Market Economy Mean?
An economic system in which economic decisions and the pricing of goods and services are guided solely by the aggregate interactions of a country's citizens and businesses and there is little government intervention or central planning. This is the opposite of a centrally planned economy, in which government decisions drive most aspects of a country's economic activity.
Investopedia explains Market Economy
Market economies work on the assumption that market forces, such as supply and demand, are the best determinants of what is right for a nation's well-being. These economies rarely engage in government interventions such as price fixing, license quotas and industry subsidizations.
While most developed nations today could be classified as having mixed economies, they are often said to have market economies because they allow market forces to drive most of their activities, typically engaging in government intervention only to the extent that it is needed to provide stability. Although the market economy is clearly the system of choice in today's global marketplace, there is significant debate regarding the amount of government intervention considered optimal for efficient economic operations.
Since the government will always have some level of regulatory control, no country operates as a free market in the strict sense of the word, but we generally say that market economies are those in which governments attempt to intervene as little as possible, while mixed economies include elements of both capitalism and socialism.
Note above that in a centrally planned economy EVERYTHING is planned by the government, i.e. how many crops are to be produced, which crops are to be produced, who get how much of the crop and in what proportion. This means that if you don't want something (ex. rice) and want something else instead (ex. bread) you have no choice in the matter as the government has made that decision for you.
Also note that in a free market economy subsidies are unheard of as subsidies are meant to either protect a producer of goods or promote the development of an industry. In a free market economy the kind of oil subsidies that exist in the States would not exist.