[Readers' comments would be most helpful here. I'm not at all sure whether I've missed detail or misrepresented some facts relating to the Term Auction Facility. Here's what I've pieced together today.]
The Term Auction Facility is an emergency provision implemented by the US Federal Reserve last December to address the freezing up of interbank lending during the so-called 'credit crisis'. The banks weren't - and aren't - using the existing 'discount window', which is the emergency facility traditionally provided. This was happening even after the Fed had dropped the rate charged. There was a lack of liquidity and something had to be done quickly.
"Lenders [were] hoarding cash and shunning their peers as if they were all lepers."  Banks had failed to mark their securities to market and there didn't appear to be any practical way to assess the real value of their assets and liabilities. Suspicions were very high after many years of unregulated/deregulated and lax lending practices. At that stage it appeared that all the good collateral of the banks had been pledged and what was left to lend against wasn't worth having.
"In the Federal Funds market the Fed, along with the Bank of Canada, Bank of England, the European Central Bank and the Swiss National Bank, decided to implement a new monetary instrument.... This program, known in the US as the Term Auction Facility, enables the Fed to auction a set amount of funds to depository institutions, against a wide range of collateral." The financial press reassured the public that the 'collateral' was of good quality and had triple A ratings from respectable firms such as Standard and Poors and Moodys. The trouble was that the rating agencies themselves had given over to the free-for-all spirit and their standards had plummeted also.
In the middle of February this year - for the first time ever - "the banking system showed negative net non-borrowed reserves" in the US . The banks were exploiting the Term Auction Facility as much as they could for a range of reasons. This was a sign of continuing distress in the financial market. The funding was cheaper than elsewhere provided. There were continuing difficulties raising funds from other sources. The collateral problems were bad and appeared to be getting worse under this new program. The bankers' greater reliance on government support resulted in the central banks increasing the amount of money they were using to fund the facility to the tune of hundreds of billions of dollars. The system lacks transparency. The public don't know who submitted the collateral. The banks are distorting their behaviour; they appear to have long begun to create Residential Mortgage-Backed Securities "and keeping them on the banks books as a quick way, in another liquidity squeeze like August , to access ECB/FED liquidity." 
The trouble is that the assets involved in these auctions have still not been appropriately valued. The solvency of the institutions involved is unknown. The true situation appears to be coming to light only after the bank is formally declared bankrupt. The public are left liable and extremely vulnerable as the Fed and other central banks accrue more and more worthless or low-value collateral.
Last night the US Fed announced that TAF "will expand by $300 billion to $450 billion."  Under the circumstances described above this is, in effect, a massive bailout of these institutions by stealth.
“If all the bank loans were paid up, no one would have a bank deposit, and there would not be a dollar of currency or coin in circulation. This is a staggering thought. We are completely dependent on the commercial banks for our money. Someone has to borrow every dollar we have in circulation, cash or credit. If the banks create ample synthetic money, we are prosperous; if not, we starve. We are absolutely without a permanent money system. When one gets a complete grasp upon the picture, the tragic absurdity of our hopeless position is almost incredible - but there it is. It (the banking problem) is the most important subject intelligent persons can investigate and reflect upon. It is so important that our present civilization may collapse unless it is widely understood and the defects remedied very soon.” - Robert H. Hemphill, Credit Manager of the Federal Reserve Bank of Atlanta
 Crisis may make 1929 look a 'walk in the park'. By Ambrose Evans-Pritchard. Last Updated: 11:02pm GMT 23/12/2007. http://www.telegraph.co.uk
 Term auction facility
From Wikipedia, on 29th September 2008
 Term Auction Facility: Confirmation of Financial Stress? Tuesday, February 19, 2008. http://www.nakedcapitalism.com/2008/02/term-auction-facility-confirmation-of.html
  A resonder to 'Term Auction Facility: Confirmation of Financial Stress?' Naked Capitalism. Tuesday, February 19, 2008. http://www.nakedcapitalism.com/2008/02/term-auction-facility-confirmation-of.html
 Fed Pumps Further $630 Billion Into Financial System (Update2)
By Scott Lanman and Craig Torres. 29th September 2008