This term is often used synonymously with the concept of "Monetary Expansion". It is a process through which the FED (or for that matter any Central Bank in any country/economy) tries to increase money supply through various methods. As a practice, it has been more popular since the Global Financial Crisis that engulfed the world over last half decade. In a situation when even when rate on interest falls to an extent that no further reduction seems viable, but still borrowers are not interested in borrowing, depositors have lost trust on banks and banks find it difficult to manage liquidity, the Central Bank comes forward with the role of a banker of the last resort to lend to the commercial bank, mortgage the securities of the commercial banks and give them money, and in the extreme case prints new currency notes (not a common practice in recent years). The basic motive is to expand the money supply in the economy so that a potential fall in GDP can be restricted in a recession by making money available in the hands of the economic agents to spend on commodities and services.
The process operate as per the famous quantity theory of money MV=PT or M/P*V =T
Where, M is the nominal money supply, V is the number of times money changes hands in a duration of time, P is the price level and T is the transactions or GDP. In a recessionary phase, since velocity of money is more or less constant for a culture depending on people's spending habits, the general Ptice level P is rigid in the short run, GDP can be increased through an expansion of money circulating in the economy.
The easiest and most commonly practised method of quantitative easing is purchase of assets by the Central Bank (FED in this case) through which the Central Bank pumps in more money in the economy and reduces the liquidity crunch.
Ari, I am not an economist. When I asked my husband (who is a teacher in the subject) about the term after reading your question, he explained this to me and I am presenting the answer as I understand it. A very useful resource is available by the Bank of England http://www.bankofengland.co.uk/monetarypolicy/Page... where you may find some more detail. I hope the answer if useful.