Stock trading is the buying and selling of shares for a predicted profit. The point of creating a stock trading market is to facilitate a meeting of investors and businesses. 
Stock trading is therefore entirely neccessary for the continued existence of a stock market. Similar to the forex trading, forex futures market, investors can choose to buy or sell stocks.
Other stock trading instruments are also available to the public such as stock options and stock index futures. A person that buys or sells stocks may be in it for the long haul or they may be just day trading.
As mentioned above, buying and selling takes place in a stock market with the intention of making a profit. However, not all stock trading markets allow the selling (Short selling) of a stock. Malaysia's stock exchange for example does not allow the short selling of any stock in its index. Investors in malaysia can only make profits when the stock in question appreciates.
The main downside to stock trading over forex trading is the initial deposit amount. With forex you can begin trading with as little as $100. With stock trading, you need to multiply that amount by 10 and you still won't have enough to make all the trades you'd like to. So stock trading is really for those that are willing to invest larger amounts from the get go. You can get a demo account but you can't really get a taste for stock trading with real funds like forex trading allows you to.
