Derivatives are any investment whose returns are based on the change in price of another investment. The most common derivatives are stock options, which allow the purchaser to either buy or sell a stock or index at a specific price in the future. Futures based on the price movement of commodities are another form of derivative.
The largest derivatives market, however, is the one that is unseen by the public. Broadly termed as synthetic options these are derivatives that are not publicly traded whose price is based on the movement of other assets that are most likely also not publicly traded. Private contracts that hedge funds make with banks, insurance company hedges in risk, institutions buying protection against downside of their portfolio all are examples of synthetics.