Basic summary as I understand it:
Corporation XYZ needs to raise short term capital (for payroll, to buy machinery, whatever).
In past, an employee (low level clerical position typically) of Corporation XYZ would call a specialist at the bond desk of a Lehman, Goldman Sachs, JP Morgan, and say 'Hey, we need 1 billion by 11 a.m. today for use over the next 30 days.'
Specialist at trading desk would say 'Okay, we will float paper today and you will have to pay face value plus 100 basis points.'
Paper would be sold in market that day, with investors receiving bond, Corporation XYZ receiving 1 billion - everyone is happy.
Now, people begin to see that there is a market for insuring the risk of default, which steals some interest on the paper, but makes the paper more marketable and 'safe' in the eyes of investors.
Hence, the 'credit swap default' is born.
Hedge funds, specialist desks at brokerage firms such as Goldman and Morgan begin to sell CSD insurance, raking in huge profits, but not being required to set aside enough capital to insure payment in the event of an actual default on the insurance they're selling.
Not only that, but entities begin to buy CDS insurance on corporations and firms whose bonds they don't even own (analagous to buying an insurance policy on your neighbors house in the event of a fire, naming you, and not your neighbor, as the beneficiary on such policy).
Also, these entities begin leveraging these CDS instruments in risky ways, by 'hedging' them, which acts as a force multiplier in terms of the risk of default (given that not enough capital was set aside by those selling CDS insurance).
When the firms whose bonds were insured against actually were perceived to become 'weaker,' 'vulnerable,' or 'sick,' the CDS buying went into overdrive - so much so that with roughly 5 trillion of corporate paper being sold at any given time, there were 60 trillion worth of CDS instruments being sold - and again, no where near even a fraction of 60 trillion of reserved capital set aside to pay on any 'defaults.'
When Bear Stearns fell, many firms that had insured against any risk of default through CDS hedging were unable to pay, creating the watershed moment of 'counter-party' risk - which caused panic as many investors began to doubt the ability of counter-parties to be able to live up to their obligations to satisfy contractual obligations;
...creating a downward cascade of a complete lack of trust in these markets, and the 'solvency' and 'liquidity' of just about any firm or bank perceived to be overly leveraged - and thus creating a resistance to even loan money between formerly transacting firms - the dreaded 'credit seizure.'