In a market economy, or a modified market economy such as the U.S. economy, production and consumption are connected in various "markets." A market is simply a place where consumers can go to buy things from producers and producers can go to sell things to consumers.
A grocery store is an example of a physical market. People who want to consume food go to the grocery store and buy it from producers through a series of middlemen. The store itself is one of the middlemen, and there are usually others along the way (distribution companies, for example). The labor market is a more abstract sort of market. In this market, businesses who want to consume work pay people to produce labor. In the stock market, consumers and producers buy and sell percentages of ownership of companies (see How Stocks and the Stock Market Work for more information).
As you can see, almost everybody is both a producer and a consumer acting in more than one market. If you have a job, you are a producer of labor. Whenever you go shopping, you are a consumer of goods.