A liquidity trap was a theoretical scenario proposed in Keynesian Economics whereby monetary policy is completely unable to have any stimulative effect on an economy, whether through lowering interest rates or by increasing the money supply.
By the 1960s most economists had come to scoff at the possibility of such a situation ever arising in reality, and by the 1980s, even Keynesian economists had begun to write the liquidity trap out of their textbooks. However, the collapse of Japan's Bubble Economy in 1990 and the ensuing "Lost Decades" of no or low growth in Japan proved that liquidity traps are very, very real.
Even when the Bank of Japan lowered interest rates to zero and expanded the money supply by more than 70 percent, Japanese borrowers were still so far underwater that they refused to borrow any more money. In real terms, interest rates were actually negative, meaning that in theory it actually cost money to keep cash in a bank, but people still kept their money in cash and cash equivalents. The liquidity preference had become virtually absolute, creating a liquidity trap.
In many ways, the United States today is in a liquidity trap. The signs are all around us. Interest rates are nearly zero, and are negative in real terms, but no matter how low they go, people will not borrow, and the economy will not grow. The yields on US treasury rates are at record lows, but still keep going lower, because the liquidity preference is so high. And recently, the Bank of New York Mellon, whose main business is acting as a bank to other banks (and the super-rich), has actually started charging its customers fees (rather than paying them interest) to keep cash in their accounts - a true negative interest rate!