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How Does Volatility Affect the Time Value of an Option?

Volatility is a key driver of an option's time value. Higher expected volatility in the underlying asset increases the probability that the option will move significantly in the money before expiration.

This higher probability translates to a higher time value and thus a higher option premium. The option Greek "Vega" measures an option's sensitivity to changes in volatility.

What Is the Difference between Historical Volatility and Implied Volatility?
How Does ‘Volatility’ (Vega) Influence an Option’s Premium?
How Does High Volatility in a Cryptocurrency like Ethereum Impact the Time Value of an ATM Option?
How Does the Dividend Yield of the Underlying Asset Affect the Value of an American Option?