Derivatives are financial instruments - that is, they are formal contracts which represent an agreement to buy something from someone. The difference between derivatives and normal financial instruments is that the value of the derivative depends on the value of something else - i.e., its value is derived from the value of another object. For example, a derivative contract may be based on the future value of a foreign currency, the market price of a commodity or something more unusual such as the weather.
The original purpose of derivatives was to reduce risk through the process of hedging. All business activities contain a measure of risk and one of the main purposes of the finance functions within a company is to manage that risk to an acceptable level (the degree to which people and companies are prepared to accept risk varies considerably). Imagine that the company signs a contract to manufacture a large number of items that it will then sell to a Japanese customer. So far so good - but what happens if the exchange rate changes between the time of signing the contract and receiving the payment. The exchange rate might go the wrong way and the amount of money received (in Japanese yen) might be worth a lot less in the future than it would be now.
Of course, it could go the other way and the company would make money but this is also a manifestation of risk and should be managed by the company. To reduce the risk, the company might take out a derivative contract on another currency that is negatively correlated with the value of the yen, for example. The American dollar usually goes up if the yen goes down, at least historically it has done so. To reduce the risk, then, the company takes out a contract to buy dollars in the future. In this way, the value of the yen sales and the dollar contract should be fairly stable, no matter which way the exchange rate goes.
Derivatives have subsequently become extremely popular in the world of finance once traders realised that they offered new ways to make money. They had particular value because the traders felt that because they knew more about the markets than other people, they should be able to make better predictions than the competition about future changes in value and, therefore, they would know how to structure the derivative to provide them with profit. One result of this is that the nature of some derivatives has become extraordinarily complicated, such that few people can actually understand what they really mean. This is also good for the traders, who do understand them, and not so good for their managers and supervisors who, as a result, have to yield more power and freedom to the trader because they cannot judge the trader's work effectively.
No doubt some people have done well out of using derivatives for arbitrage - that is, buying and selling with a view to making a profit. However, there are also many stories of people (and large companies, for example Barings Bank) being ruined by the unwise use of derivatives. Not only is it fundamentally impossible to predict the future accurately and consistently, but the nature of a derivative is necessarily that some will win and some will lose. It is little different from gambling.
