This NPR article is mainly a transcript of the CDS part of this American Life podcast. And I found the explanation using examples very good. I copied below 3 extracts:

• Credit Default Swap as insurance: 

Imagine, he says, you buy a bond from Ford for $100.

"You’re holding your bond and you are worried about Ford’s credit. So you enter into an agreement with another party where you say to other party, ‘I will pay you some money — 2 percent a year, 3 percent, 4 percent — and what you need to do is give me protection.’

"If Ford should go bankrupt, then I’m going to give you this perhaps worthless bond and you’re going to give me my $100 back. In the big context, it looks like insurance."

• Credit Default Swap as gambling:

"The way that I first described the credit default swap is, you own the bond and you want to transfer the risk to someone else. But what if I want to buy protection but I don’t own the bond?" Berman says. But isn’t buying protection on a bond you don’t own like buying fire insurance on a house that’s not yours? "It is exactly like buying insurance for a house you don’t own," Berman says. "So it’s like you took out fire insurance on your home, and I also took out fire insurance on your home, and a thousand other people took out fire insurance on your home.

"And when that happens, what you’re doing is, you’re betting on the house."

• Credit Default Swap and Leverage:

Imagine someone with a hedge fund worth $100 million who wants to make a killing in the credit default swap market. He starts calling and e-mailing all those credit default swap desks and hedge funds out there, saying, "I’m selling protection, who wants to buy?"

Someone calls back and says, "I have a billion-dollar bond from Lehman Brothers, I want to insure." He says, great, "I’ll insure your bond if you agree to pay me 2 percent of its value every year." The caller says, "All right." They are in business.

Now, let’s review those numbers: 2 percent of $1 billion is $20 million, which the person with the $100 million hedge fund gets every year. So, by signing one piece of paper, he has doubled his money in five years — psyching him and his investors.

That’s the upside of leverage: You make profits on a billion dollars even though you only have $100 million.

The downside of leverage is that he is on the hook for up to $1 billion if the bond defaults and he doesn’t have a billion.

How Credit Default Swaps Spread Financial Rot : NPR