A Stock Market is a public market with the purpose of trading of company stock at an agreed upon price
. Companies that are traded publically are traded on the Stock Market. A stock represents the ownership of a company's assets and profits. So when someone what to sell shares of their company they would issue stocks. If these stocks are publically traded they would be bought and sold at a Stock Market or also called a stock exchange. A stock exchange also buys and sells shares and other such securities.
There are a large number of stock exchanges all over the world. The largest stock market in the United States is the New York Stock Exchange or NYSE which has been in business for the trading of stocks for over 200 years. This is a physical market at a physical location where traders on the floor of the stock exchange respond to calls of buy or sell. Another type of stock exchange is the NASDAQ which is a virtual stork exchange where the stocks get bought and sold in cyberspace. But the stocks are bought and sold by the same process and all stock exchanges are reported linked instantly by internet.
If you want to buy stocks you would call on a stock broker who is licensed to buy and sell stocks at a stock exchange. You would not have to physically visit the stock exchange to buy and sell your own stocks. You can also do online stock buying and selling but al of these transactions go through some kind of stock broker whether a full services broker or a discount broker.
Because the trades of a stock take place at a stock exchange the status of every stock traded is instantly known. You can follow this action on a minute by minute basis if you so choose. You can also see how when something happens to a publically traded company the company's stock value may go instantly up or down based on the information received. And there may be literally thousands of people who are buying and selling stock on a Stock Market at any point in time when the stock exchange is open. Of course the stock exchange does shut down and is closed on public holidays or sometimes it is shut down when a national disaster takes place such as the 9/11 attacks.
In a publically traded company, all of the company information is made public so if you are going to buy or sell a company's shares you will have access to a vast amount of public information. A public company is regulated by the US Securities and Exchange Commission. So someone who buys and sells a publically traded company's stocks on a stock exchange has some knowledge about that company. They also have some reassurances that the company is handling itself per the SEC guidelines.
There are stock exchanges in most major cities in the US and around the world such as London, Paris, and Tokyo to name a very few.