What is a liquidity trap?
One of the options of the monetary authorities to deal with a situation of economic stagnation with falling prices is to inject money into the economy. This increases consumption and investment and, as a consequence, employment. This is called expansionary monetary policy.
The liquidity trap is defined as a situation in which interest rates are very low (even 0 or negative), so that people accumulate money instead of investing or spending it. In such a situation, the increase in the money supply (money in circulation) has no effect on the economy.
Keynes was the first to speak of the liquidity trap, and to explain how, in such a situation, increasing the money supply becomes ineffective in varying interest rates and reviving the economy. To get out of the liquidity trap, Keynes proposed implementing an expansionary fiscal policy, using increased public spending as a lever to improve GDP and employment. Such policies cannot always be implemented, because in a crisis situation, where the public sector is heavily indebted, it is difficult to implement such policies. However, Paul Krugman is in favor of increasing inflation until people's fear that their savings will lose value due to inflation leads them to consume and invest, thus stimulating the economy.
In the image we can see the graphical representation of the liquidity trap: The increase in the money supply (M), in an economy with "normal" interest rates, causes a decrease in interest rates and therefore an increase in spending and consumption. We see that when interest rates can no longer fall, an increase in the money supply will have no effect on them and therefore consumers will prefer to keep their assets liquid and neither consumption nor investment will be encouraged.