An option is a derivative security, where the cash flows are a function of the underlying S.

A call option is a right, but not obligation, to buy a given quantity of the underlying security at a given price, called the exercise price K, within a certain time horizon.

A put option is the right, but not obligation, to sell a given quantity of the underlying security to an agreed exercise price within a given time interval.

 If an option can only be exercised at a given date, the option is called an European Option. If the option can be exercised at any moment during a whole time period up to a given date, the option is called American option.

An option will only be used if it is valuable to the option holder. In the case of a call option, this is when the exercise price K is lower than the price of the underlying S.

Hence, options have never negative cash flows at maturity.

Thus, for anybody to be willing to offer an option, they must have a cost when entered into. This cost, or price, is typically called an option premium.