A market system is one in which the basic economic questions are answered by the forces of supply and demand. Consumers and producers, through their own actions, determine how these questions will be answered.
The basic economic questions are 1) what will the economy make, 2) how will it make those things, and 3) for whom will it make them. In a market system, these questions are answered not by government fiat but by the forces of supply and demand.
In a market system, consumer decisions affect what will be made and how it will be made. If a supplier makes a certain product, consumers decide whether to buy it. If many consumers buy it (if demand is high), its price rises. This signals to various producers that they should make that product. Whichever producer can make the product in the best way will be able to sell more of that product than the other producers. In this way, consumer decisions decide which products will be made and how they will be made.
Producer and consumer decisions also determine who gets the products that are made. Producers decide if they will try to sell to upscale markets or lower-income markets. Consumers decide whether they want to buy certain things.
This is what characterizes a market economy. It is one in which consumers and producers make decisions that affect supply and demand and prices. The signals sent by the prices help to determine what things will be made, how, and for whom.