A derivative is a broad category of securities, based on the price of an underlying asset. It is a contract between two parties based upon an asset where the price or value fluctuates. Common types of derivatives are stocks, bonds, currencies and market index. In the simplest of terms, a derivative is a bet between two parties based on whether the value of an asset will increase or decrease over time.
Future contracts, or futures, is a common form of a derivative. In this scenario, the buyer and seller agree to a price for the asset, but the sale will not happen until a future date is reached. The seller is hedging their asset against loss. They are betting the future price will go down, while the buyer is betting it will become more valuable. Farm futures on crops and cattle are very common due to the constant flux of these products.
Options are another form of future contracts. The two parties agree to the future, but either party can "option" not to complete the contract.
Swaps are a form of derivative often seen in the credit market. These are usually interest rate swaps. Companies may swap terms with another company to achieve a better debt ratio within their own company or increase cash flow. The risk is the other company defaulting on the loan.