(Also see: short sale)
Being "short" a stock is the state of having sold a stock or futures contract without covering it. Being short is also known as "taking a short position." It is the opposite of being long (or having a long position). A short stock sale is one in which someone is selling shares he or she does not actually own. Instead, his/her brokerage firm borrows the shares from another investor, with that investor's permission.
A short seller sells a borrowed security, commodity or currency with the expectation that it will go down in value. The investor must eventually return the borrowed stock by buying it back on the open market. If the investor can buy it for less than he sold it, he makes a profit.
In options trading, a short position is the writing (or sale) of an option contract. Someone who has written a call or put option is short that contract and has the obligation to fulfill its terms if assigned an exercise notice. 
- Course: Options Basics. Options Industry Council.