A short squeeze is when many people who have sold a stock short buy back shares at the same time.
When many investors have sold short a stock on the hope that its price will plunge, that price may begin to rise. As it does so, more and more of these "shorters" will "cover" their investments. That is, they'll buy back the shares that they had shorted, and take a loss, since they're having now to buy the shares at a higher price. As more and more shorters do this, the price rises (since more people are buying than selling). In a nutshell, this is a short squeeze.
Remember that a short position starts with borrowing (through your broker) the shares of stock you've sold. The brokers who have loaned out the stock can also require the short-sellers to return the shares, meaning that the shorts must buy the stock themselves or risk a forced "buy-in" by the brokerage firm (that is, the broker buys back the stock for you). Because brokerage firms aren't very picky about paying a good price on such occasions, the stock can spike dramatically, especially since market makers responsible for providing liquidity for a stock often see forced buy-ins as an opportunity to make a quick killing by temporarily raising their prices. Forced buy-ins may result from a trade going so much against a short-seller that he gets a margin call from the broker to either put up more cash or risk losing the position. Other times, it simply represents a change in short-term supply and demand exacerbated by increased trading volume and rapid turnover.
Let's say a heavily shorted company announces positive news that brings in new buyers. This demand pushes the stock higher, but it also leads some old holders to sell. The stock moves from one broker to another. Short-sellers who had borrowed shares from these old holders may have to cover the short position if their broker can't find new shares for them to borrow. This creates more demand, which pushes prices higher and continues the process. As you might expect, short squeezes often come in waves that attract momentum-oriented investors who see a stock rising and jump on for the ride. This additional demand, in turn, exacerbates the squeeze. Of course, these momentum investors usually jump ship quite rapidly when the momentum changes, adding to selling pressure later.
Of course, when the buying pressure stops, the stock price often falls back down to where it was before the squeeze happened, or even further.
Companies can try to reduce the number of shares sold short by encouraging their shareholders to "take delivery" of the shares. That is, move the position from the margin account to a cash account. (Shares in a cash account cannot be borrowed, so they aren't available for shorting.) Of course, the best way for a company to get rid of shorts is to provide good earnings and other results from their business operations, leading to a rise in the stock price that way. If the company is resorting to tactics like the above, it's probably time to leave as a long investor.
Another item to watch for is investors who invest in the hopes of a short squeeze. That would, of course, allow them to exit their position at a higher price, but it is a sign of desperation and long investors should probably avoid those companies, too.
The ultimate short squeeze occurs when some savy investor manages to corner the market in that security making it impossible to cover the short position. Short sellers can take unlimited losses, because theoretically the market value of the stock becomes infinite. Stories are told of famous investors who managed to corner various markets from time to time. The risk of this development is not very high in modern times, but shorts should not sleep too soundly.