Options are derivative products that derive their value from an underlying asset. They can be built around a wide-range of underlying assets (or variables), including stocks and indices as well as more obscure assets built around the weather, for example.
A Call Option provides the holder with the right, but not the obligation, to buy an underlying asset at a predetermined price on a pre-specified date.
Similarly, a Put Option provides the holder with the right, but not the obligation, to sell an underlying asset at a predetermined price on a pre-specified date.
So, these options provide the holder with the opportunity to profit from exercising the option (by buying the underlying asset at less than its current spot value, or selling the underlying asset at more than its spot value) without having the obligation to exercise. Effectively, options deliver a payoff profile which only has upside (as you wouldn’t exercise the option if you couldn’t profit from doing so).
At the time of expiry, the payoff to the holder of a call option will be the underlying asset price at expiry minus the predetermined strike price, and vice versa for the holder of a put option.
As an option provides the right, but not an obligation to buy (with a call) or sell (with a put) the underlying asset, the buyer of an option must pay a premium – the price of the option.