A future (formally known as a futures contract) is a kind of derivative often used to take “bets” on the price of something increasing or decreasing. If an individual believed the price of something [a commodity or stock, for example] was going to change in the future, they could buy a future for that item and make money if the change in price occured.
A derivative is a financial product that functions very similarly to a stock. Anyone can buy a derivative, and the value of it depends on the value of the underlying asset. For example, the value of a gold derivative is derived from the price of gold. If the price of gold increases, the value of the gold derivative increases.