"Squeezing the shorts" refers to a questionable practice in which a trader takes advantage of a stock that has been short sold substantially by buying up large blocks of the stock. This causes the stock's price to increase and forces short sellers to attempt to buy the stock in order to close out their positions and cut their losses. However, because the trader has bought up large blocks of the stock in question, the short sellers may find it very difficult to buy stock at a price that they prefer. The trader can then sell the stock to the desperate short sellers at a higher premium.
Squeezing the shorts can also be done with commodities that are traded through futures contracts. In this case, traders would take long positions in the futures contracts involving a certain commodity at a low price and then would try to purchase the entire supply of that same commodity. If the trader was successful, anyone who was holding a short position in the futures contract would have to buy the commodity at a higher price just to be able sell it back at a lower price, which is clearly an unfavorable outcome for a short-sale transaction.
Squeezing the shorts is very difficult to achieve. For example, in the 1970s, Nelson Bunker Hunt tried to squeeze the shorts in the silver market. At one point, Hunt and his associates had acquired more than 200 million ounces of silver, which caused silver prices to move from around $2 per ounce in the early 1970s to nearly $50 per ounce by 1980. Unfortunately for Hunt, maintaining a stranglehold on an entire market is very difficult. In this case, regulators decided to put a stop to Hunt's manipulation by implementing higher margin requirements and limiting the amount of contracts that any one trader can hold. Eventually, Hunt's scheme failed and he was forced to declared bankruptcy.
To learn more about futures, see Futures Fundamentals