You pay a small premium every quarter. If the company it's written on actually defaults, you get paid a large sum. If it doesn't, you've just paid for insurance.
A CDS is insurance on debt. The protection buyer pays the seller a regular premium (the "spread"); in exchange, if the reference entity — the company or country the contract is written on — has a credit event, the seller pays the buyer for the loss.
"Credit event" usually means default, but can also cover a restructuring or a missed payment, depending on how the contract is written.
A bank holding a company's bonds can buy CDS on that company instead of selling the bonds outright — it keeps the position but removes the default risk.
Others buy CDS with no underlying bond at all, purely as a bet that a company's credit is about to deteriorate — or sell it purely to collect premium from a company they think is safe.
Banks hedging loan books, bond investors managing credit risk without trading the bond itself, and hedge funds taking outright views on which companies — or countries — are headed for trouble.
CDS spreads are watched closely because they tend to move faster than credit ratings do.