In a fiat world, money is printed into existence by the central bank - in the United States the Fed. Given there is nothing backing up this money, it is inherently worthless. However, one can think of as real. It was printed (even if only electronically), therefore it exists.
In addition to the previously mentioned money supply, fractional reserve lending allows credit to be extended by banks and financial institutions on top of that inherently worthless money. Indeed, banks and financial institutions have leveraged credit to base money at ratios of 30-1, 50-1 or even higher.
It's pretty amazing if you think about it: Credit is extended with 30-50 times leverage on inherently worthless paper.
Ponzi Financing
Borrowers have to pay interest on the amount borrowed. However, the interest and the debt cannot possibly be paid back except by an ever expanding Ponzi scheme of lending. That scheme can last only as long as everyone believes the debt can be paid back and the market value of that debt keeps rising.
It's a faith based system in which banks extend loans and hold the credit on the books (or in many cases off the books in various structured instruments). The banks are thought of as being well capitalized as long as the value of credit on the books in relation to their reserves meets some ridiculously low minimum set by the Fed.
This is how the system works, using the term "works" loosely.
Day of Reckoning
The day of reckoning comes when asset prices start falling, defaults soar, and the value of credit on the books starts plunging. That day of reckoning has arrived.
http://globaleconomicanalysis.blogspot.com/2009/02/fiat-world-mathematical-model.html