A derivative is a financial instrument that gets its value from some real good or stock. It is, in its most basic form, simply a contract between two parties to exchange value based on the action of a real good or service. Typically, the seller receives money in exchange for an agreement to purchase or sell some good or service at some specified future date.
The largest appeal of these instruments is that they offer some degree of leverage. Leverage is a financial term that refers to the multiplication that happens when a small amount of money is used to control an item of much larger value. A mortgage is the most common form of leverage: for a small amount of money and taking on the obligation of a mortgage, a person gains control of a property of much larger value than the small amount of money that has exchanged hands.
Derivatives offer the same sort of leverage or multiplication as a mortgage. For a small amount of money, the investor can control a much larger value of company stock than would be possible without use of these instruments. This can work both ways, though. If the investor is correct, then more money can be made than if the investment had been made directly into the company itself. The losses are multiplied instead, however, if the investor is wrong.
This type of financial instrument made the news in 1995 when rogue trader Nick Leeson single-handedly caused the failure of the Barings bank of England. Nick Leeson was a derivatives trader whose trades did not work out and, due to the enormous leverage of the trades used, the losses became so large that the bank went bankrupt. Warren Buffett, a much revered and very successful investor, has stated in one of his annual reports that he is very much against the use of these instruments, and he expects that they will lead to eventual failure for anyone who uses them. In spite of all this negative press, however, they have long been a normal part of business and investing and are likely to be so for many more years.