Most people think about trading stocks in the "long" fashion. This is when you buy a stock, hold on to it for a period of time, then later sell it (hoping that the price is higher than when you bought it.) It's the way most individual investors trade stocks and it's pretty easy to understand.
Short trading is a little trickier. Shorting a stock is basically borrowing shares of a stock and promising to give them back later. After you borrow the stock you sell it. This is called "short selling". Then eventually you must pay the shares back to wherever you borrowed them from. You have to buy them back, hoping that the stock is cheaper now than when you sold it. This is called "buying to cover".
"short selling" = selling a stock you don't own and you have to buy it back later
"long selling" = selling a stock after buying it yourself
