We hear a lot of irrational worries about the derivatives market. The truth is derivatives drastically reduce systemic risk for markets; they don't increase it. There are a great many people who think derivates do the exact opposite—serving to destabilize markets. But they are wrong. And fear of a falsehood is bullish.
A derivative is simply a type of contract. Its price is derived (pun intended) from a movement in the price of something else—usually a stock or some other kind of security. So the value of a derivative depends on the value of something else.
The difference between a naked and covered derivative is probably the most misunderstood element on this topic. A naked derivative occurs when someone buys the contract as a leveraged way to make a bet on something else going up or down a lot in price to achieve a big, quick profit. This can be a very risky enterprise because, of course, you could also lose a lot, too, and just as quickly.
The other is when someone has a risk, like a loan perhaps, and uses a small amount of capital to offset the risk partially or completely by purchasing a derivative. That's a covered derivative, and it's by far the most prevalent among financial institutions. If you have a lot of stocks that act a lot like the S&P 500 and you buy a simple derivative like a S&P 500 put option, you can reduce your risk without selling your stocks while paying a price for that insurance-like effect (called a premium) and then you still have upside potential, just less than if you hadn't paid the premium.
Let's look at a specific example. Suppose Dell plans to buy $10 million in semiconductors from a company in Taiwan in the next two years. Once purchased, Dell plans to use those semiconductors to build computers, which will be sold to customers in continental Europe. If the Taiwanese dollar increases in value before Dell pays for the semiconductors, the semiconductors will cost more than they originally anticipated in terms of US dollars. Dell can reduce its currency risk by entering into a derivatives contract that gives the company the right to buy Taiwanese dollars at the current exchange rate two years from now.
These sorts of activities, and literally millions of others like them, allow investors to mitigate risk. Derivatives in aggregate serve this very useful, and necessary, function in the continuing development of capital markets.