A derivative is the collective term used for a wide variety of financial instruments whose price derives from or depends on the performance of other underlying investments, typically bonds, equities, commodities or currencies. Derivatives are essentially a bet on which way the price of an underlying investment will go, which means that you can make money on them whether the market goes up or down.
As such, they can be used either to gamble or to reduce the risk of ('hedge') an investment in the underlying security. Examples of derivatives are futures, options and swaps. For instance, an option is a derivative because its value changes in relation to the performance of an underlying stock.