If you buy shares of a stock, you are considered as being "long" in that stock. I.e. you bought shares, and you will potentially sell them in the future to someone else, hopefully after they have appreciated in value. However, you do not have to sell the shares and they theoretically could be passed to your heirs, the heirs of your heirs, etc. in perpetuity as long as the company is still around that long.
Short selling, or "shorting," a stock is when you borrow shares you don't own and "sell" them. Later on, to cover your short, you must buy shares back at the then prevailing price to "repay" the shares your shorted. When someone shorts a stock, it is because s/he thinks the stock is going to go down in value - essentially, you "sell" them now and hope the shares decline in value such that you can "buy" them back at a later date and lower price to "pay back." It can be an extremely risky strategy because there is technically no limit to how much money you can lose.
For example, if you go "long" in 100 shares of XYZ company at $50/share, the most you could lose would be your original $5,000 investement (100 shares x $50/share) if the price per share went to $0. There is theoretically no limit to the amount of money you could make, as the stock price could rise infinately. So, you are limited to the down side (i.e. you cannot lose more than the original investment), but you are theoretically not limited to the amount you can make.
On the flip side, if you "short" 100 shares of XYZ company at $50/share, it means that you have borrowed shares and sold them for $5,000. If the price went to $0.00, you would effectively be able to "buy" 100 shares of XYZ for nothing (or in reality, close to nothing) to cover your short, and you would have made $5,000. You essentially bought them for nothing and sold them for $5,000 - you just did it in reverse order from the normal buy and then sell.
However, if the share price goes up and/or never goes below the $50 you "sold" the shares for, you would lose money. Let's assume again that you short XYZ at $50/share (so you receive $5,000 from the "sale") and the price goes to $100/share. If you are going to cover your short, you would have to "buy" the shares for $10,000 to pay the shares back, meaning that you have lost $5,000 on the transaction - if we flip it, you've essentially bought the 100 shares for $10,000 and sold them for $5,000.
Therefore, in direct contrast to going "long" (where there is a maximum that you can lose), when short selling, there is a maximum amount you can gain (which would be the price per share when you shorted the stock - $50 in the above example - minus $0). Also, in direct contrast to going "long" (where there is theoretically no maximum to the amount that you can make), when short selling, there is theoretically no maximum to the amount you can lose (if you short at $50/share and the share price goes up infinately, then you could continue to increase your loss).
This is why short-selling can be an extremely risky strategy. There are ways to hedge against potential short sale losses, but even when you do that, it still remains risky.
For a more detailed description of short selling, check out this tutorial at Investopedia.
Hope that helps some.
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