The market is where people buy and sell shares of companies. It is equivalent to a big mall where instead of buying shoes and pretzels , you can directly buy part of a company. Owners of a private company will put up some of their ownership for sale to the public in the form of stocks.
The market then facilitates or eases the buying and selling of these stocks sold to the public. When people buy the stocks they become part owners of the company. If the company performs well, the stock will go up , if the company performs poorly the stock will go down.