They don't insure individual mortgages. The generally insure mortgage backed securities, corporate bonds, municipal and state bonds, and large denomination loans.
Here's an explanation I wrote a few days ago for someone with the same question:
http://www.democraticunderground.com/discuss/duboard.php?az=show_topic&forum=114&topic_id=59768#59789Unfortunately, these derivatives are exotic and many people writing about them don't know what they are talking about. For example, I was really disappointed in the Village Voice article which gets it mostly wrong.
JakeXT's post above has a good explanation in the first article in the first few paragraphs. Problem is that people who get it get so angry that they then launch into the bigger issues/problems which muddy the explanation you are looking for.
So here's the stripped down version.
"Credit" simply means a loan or debt in financial language.
"Default" means a breaking of a contract. In this context, the contract is the debt contract. So failing to pay interest on time is a "default."
"Swap" mean just what it means on the playground when you swap baseball cards. Two people (or parties) exchange something.
So a "credit default swap" is a type of contract where a lender who would ordinarily suffer the consequences when his debtor or borrower "defaults" and fails to pay interest on time, "swaps" that risk with someone else for a fee.
Suppose you are a pension fund manager. Most pension funds gather money from employees and invest it for the long term. Because they are regulated, they have to make very, very conservative investments, mostly in bonds. Investing in bonds, that is, buying a bond from some company, is the same as lending that company money. The company takes the money, promises to pay interest every year, and then pay back the entire debt or amount of the bond, some time in the future, usually 5 years or 10 years or 20 years or whatever. Those bonds that pension funds invest in have to be very safe. The pension fund manager knows they are safe because a rating agency tells him so (ha, ha ha!) by rating the bond as triple A ("AAA rating").
But very safe bonds usually don't pay very much interest, maybe 3%.
There might be riskier bonds available that pay higher interest, maybe 6%, but legally the pension fund manager can't invest in them. Let's call them RiskyCorp bonds. Each RiskyCorp bond is $10,000 and pays 6% per year or $600. RiskyCorp bonds are not AAA rated, but BBB rated.
So a big bank or insurance company (let's call it Goldman) will offer a credit default swap to the pension fund manager. Goldman will say, if you buy 1 RiskyCorp for $10,000 and give me $100 of your $600 annual interest on the bond, I promise that in the future if anything bad happens to RiskyCorp (it "defaults") , I'll make sure that you get your $10,000 back.
That's the basics of a "credit default swap" contract.
So now Pension can pay RiskyCorp $10,000 for a RiskyCorp bond and gets $600 interest minus $100 fee to Goldman or $500 per year, which is better than $300 he would have gotten from a triple A bond.
A government regulator might say to Pension fund, wait a minute, you are only allowed to invest in AAA bonds, and you bought RiskyCorp bonds and they are BBB, not AAA.
Pension fund can say my risk on the bond should not be measured by RiskyCorp, but instead by Goldman because if anything bad happens to RiskyCorp, Goldman, not RiskyCorp has to pay up. Goldman is a big investment bank and its bonds are AAA rated.
This is another meaning behind the term "credit default swap." Notice that RiskyCorp and Goldman have "swapped" credit ratings as far as Pension fund and its regulators are concerned. Pension fund is now only concerned with Goldmans credit rating, not RiskyCorp's.
So now, let's say that RiskyCorp does indeed default and stops paying interest. RiskyCorp bonds are selling on the bond market at $2,000 instead of $10,000 because most investors think RiskyCorp cannot come up with the $10,000 per bond it owes.
Pension fund can take its now almost worthless RiskyCorp bond to Goldman and say, RiskyCorp has now defaulted. By presenting the bond and the credit default swap contract to Goldman, Goldman must pay Pension fund $10,000.
There are lots of problems with this system.
If Goldman had been selling insurance, it would be regulated like insurance, and would have had to take the $100 annual fees from all the people it sold cds to, and put it in the bank as a insurance "reserve". But because of something Phil Gramm inserted into federal law, cds were not regulated as insurance, but were treated as derivatives. That mean that Goldman could pocked the $100 as profit without setting aside a reserve.
Worse, if Goldman begins to look shaky, then Pension funds and other investors all across the country and the world who thought they had super safe AAA rated insured investments now don't. They have to dump all RiskyCorp type bonds into the market and take their losses.
This is why the Treasury and Fed are so hell bent on paying off AIG's credit default swaps and assuming their debts.
Another truly terrible thing about the system is what Goldman does to protect itself. Goldman does not put its fees into the bank as reserve, but contrary to much popular uinformed writing on this topic, Goldman does not do nothing to protect itself.
It does some crazy, dangerous things to protect itself from RiskyCorp's bad credit. For example, it will itself turn around and buy a credit default swap from, say AIG or Lehman. Or worse, it will try to hedge it's risk from RiskyCorp by "hedging." Hedging means making an equal but opposite trade. To hedge the risk of RiskyCorp going bankrupt, Goldman will engage in "dynamic hedging," which is a form of complicated short selling that actually makes it more likely that RiskyCorp will indeed go bankrupt.
It's as though your insurance company that insures your house comes over to your house and burns it down. It's that bad.