A "liquidity trap" is where interest rates are zero, and so cannot be reduced any further, even if that is necessary to stimulate growth. In most developed countries, the cash (discount) rate is at or very close to zero. Stimulating growth requires further monetary stimulus, and the current technique is called QE (quantitative easing) where the central bank buys long-dated government stock to drive down long term interest rates. But that hasn't been very effective.
The last time we had a liquidity trap on the scale we now do was during the great depression. In this article, Nicholas Crafts shows how the government stimulated the British economy using unconventional measures.
In mid-1932, the UK had experienced a recession of a similar magnitude to that of 2008-09, was engaged in fiscal consolidation that reduced the structural budget deficit by about 4% of GDP, had short-term interest rates that were close to zero, and was in a double-dip recession (Crafts and Fearon 2013). The years from 1933 through 1936 saw a very strong recovery with growth of over 4% in every year. The Chancellor of the Exchequer, Neville Chamberlain (in office from November 1931 to May 1937) was the architect of this recovery.
Disclaimer. After nearly 40 years managing money for some of the largest life offices and investment managers in the world, I think I have something to offer. These days I'm retired, and I can't by law give you advice. I do make mistakes, but I try hard to do my analysis thoroughly, and to make sure my data are correct. Remember: the unexpected sometimes happens. The expected does too, but all too often it takes longer than you thought it would.
The Goddess of Markets punishes (eventually) greed, folly, laziness and arrogance. No matter how many years you've served Her. Take care. Be humble. And don't blame me.
BTW, clicking on most charts will produce the original-sized, i.e., bigger version.