Basically it is an exchange place or a market that facilitates the trading of stocks. People participating in the stock markets range from some casual traders and investors who trade as a hobby, to large fund traders.
In India the most famous exchanges or markets are the Bombay Stock Exchange (BSE) and the National Stock Exchange (NSE). Globally there are many markets including the famous New York Stock (NYSE), NASDAQ, London Stock Exchange, Hong Kong Stock Exchange etc..
Any market can be thought of with two functionalities:

Primary Market: Here the companies and industries raise long term funds for their operations by issuing shares. Companies come up with an initial price, mostly with premium for the face value of the shares, which will be distributed to the investors. This is called the Initial Public Offer or the IPO.

Secondary Market: After a Company has finished its IPO, it is listed in the markets. After getting listed and issued shares to investors, the shares can then be sold to other investors in the stock market. Here the people can buy the shares at a current price as determined by other investors in the market.