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.