Derivative refers to a security whose value depends on the value of another asset. For example a warrant is a derivative based on the value of the equity that the warrant can be used to buy.
Derivatives can be used to get exposure to the underlying asset without having to put up all of the cost of buying the asset itself – they can be a lot riskier than buying the asset but this is not always the case.
For example, different combinations of derivatives can be used to protect the downside on an investment or benefit from volatility in the price of the asset. They can be hard to understand, however, and sometimes hard to value.