Explain the Relationship between Implied Volatility and the Premium of an Option

Implied volatility (IV) is the market's expectation of the underlying asset's future price movement, and it is the single most important factor driving an option's premium. There is a direct, positive relationship: as implied volatility increases, the option premium (price) increases, all else being equal.

This is because higher IV suggests a greater chance of extreme price movements, increasing the probability of the option expiring in-the-money.