Note: You can also watch a phenomenal short video as an introduction to derivaties. This is recommended for people who already have a bit of understanding in this regard.
Derivative: A financial contract, whose value depends on it's underlying assets.
For example, an apple pie is a derivative of an apple as it is derived from the apple and the price of the apple pie is determined by the quality and quantity of the apples used to make it (among other things).
Similarly, the price of a financial contract that is derived from some underlying assets such as shares of stock is determined by the quality,quantity and current price of the underlying asset and is known as a derivative.
Derivative are of 4 types: