Time value

Any option price splits into two pieces. Intrinsic value is what the option would pay if it expired this second, which for a call is the underlying price less the strike floored at zero, and for a put is the strike less the underlying price floored at zero. Time value is everything else in the price.

Time value is what you are actually buying when you buy an option that is not yet in the money. It is the market's price for the possibility that the underlying moves far enough before expiry to put the option in the money, and it rises with the time remaining and with the volatility of the underlying, since both increase the chance of that happening.

It also explains a fact that puzzles people: an option is generally worth more alive than exercised. Exercising an American call early converts an instrument worth intrinsic plus time value into one worth intrinsic alone, which is why early exercise is usually irrational absent a large dividend.

At expiry time value is zero by construction, so the option is worth exactly its intrinsic value and not a cent more. Everything between issue and expiry is the market repricing that remaining chance, which is why an option can lose money for its holder even when the underlying moves in the right direction, if it does not move far enough or fast enough.