The modern financial system is debt based. Since 1971, the financial system has had no tie to gold or any other physical standard. Through fractional reserve banking, money is created through the issuance of debt. The more debt that is issued, the more money there is, and the more demand there is for goods and services (if you believe the quantity theory of money).
As long as the system is growing, the system works well, because paying back debts with interest does not put too great a strain on the system. Want to see why? Look here.
When the economic system is growing, it is possible to pay back debt with interest, because even after paying interest, there is enough money left for other things.
For a business or government rolling over debt, cash flow continues to increase. When the economy hits limits, such as an oil supply that cannot grow fast enough to support the growth needed to keep the treadmill going, repaying the debt with interest becomes a huge burden. These graphs are from the Oil Drum, and they illustrate the point nicely.
The Irish economy is forecast to contract by 4-6% this year (i.e., GDP growth will be be negative), and we are in a deflation of at least 2-4% as well, so prices are falling, making the real value of our cash balances rise, but also making our borrowings that bit more expensive. This happened in another country, not too long ago. We live in interesting times.