It's a given in the marketplace that a stock will vary in price throughout the trading day. With each successive trade, the price can go up or down, or remain unchanged.
If you review a stock's daily closing prices over a period of time, you can observe these net changes, also called returns. These changing, or fluctuating, trading prices represent a stock's volatility. Volatility doesn't represent a bias for up or down price movement, but just fluctuation over a period of time. The degree of fluctuation can vary whether a stock's price trend is bullish and advancing, bearish and declining, or remains in a steady range over time.
As a derivative security, an equity option's value is determined largely by its underlying stock price. So when you value an option on any given day, the current stock price is crucial. But so is the expected stock price behavior over the lifetime of the option - specifically where the stock could be trading before and at expiration.
When they use an option pricing model, such as the well known Black-Scholes model, to price calls and puts, investors and option professionals alike rely on the stock's volatility factor to assess what those prices might be.