Derivatives are financial instruments derived from an underlying security (known as the underlying cash market). There are three main types of derivative: futures (forwards), options, and swaps (including credit derivatives).
The main use of derivatives is to reduce risk for one party. Derivatives can be based on different types of assets such as commodities, equities (stocks), bonds, interest rates, exchange rates, or indexes (such as a stock market index, consumer price index (CPI), or even an index of weather conditions).
A future (also called a forward) is a forward contract, i.e. an agreement to take delivery of something on a particular date at an agreed price.
The futures markets allow you to trade on margin, which allows traders to command a much larger market position than the margin amount.
An option is the right, but not an obligation, to take delivery of something on a specific date in the future at a price agreed now.
A swap is a derivative with which two separate parties agree to exchange one stream of cash flows against another stream. These streams are called the 'legs' of the swap.
The cash flows are calculated over a notional principal amount, which is usually not exchanged between counterparties. Consequently, swaps can be used to create unfunded exposures to an underlying asset, since counterparties can earn the profit or loss from movements in price without having to post the notional amount in cash or collateral.
Swaps can be used to hedge certain risks such as interest rate risk, or to speculate on changes in the underlying prices.