Derivatives are financial contracts, which derive their value off a spot price time-series, which is called "the underlying". The underlying asset can be equity, index, commodity or any other asset. Some common examples of derivatives are Forwards, Futures, Options and Swaps.
Derivatives help to improve market efficiencies because risks can be isolated and sold to those who are willing to accept them at the least cost. Using derivatives breaks risk into pieces that can be managed independently. From a market-oriented perspective, derivatives offer the free trading of financial risks.