Stock options come in two varieties. A call option is the right to buy a given asset at a fixed price on or before a specific date. A put option is the right to sell a given asset at a fixed price on or before a specific date. The asset to be bought or sold is called the underlying, the exercise price or strike price, is the price at which the underlying will be bought or sold, and the expiration date is the point in time when the option may no longer be exercised.
Options are generally priced using the Black-Scholes model. It combines the time remaining until expiration, the strike price, the current price of the underlying and an estimate of future volatility known as the implied volatility (IV) to generate a theoretical price for an option.
Because implied volatility is the only unknown input, proper options pricing is entirely dependent on accurate forecasts of future volatility. The usual approach is to measure the actual volatility of the underlying over the recent past, adjust for anticipated news events such as an upcoming earnings release, and add some margin for safety. This approach works fairly well for liquid (heavily traded) options.
Options pricing for strike prices a long way from the current price of the underlying is a little trickier. Partly as a reflection of their lower liquidity, and partly as acknowledgment that unexpected large price movements can and do happen, such options have an additional level of margin added to their price.
This results in something referred to as the "volatility smile". Black Scholes can be used in reverse to calculate the implied volatility (IV) necessary to generate a given price; graphing the IV for a wide range of exercise prices will result in a plot resembling a smile. That is, the further the exercise price from the underlying price, the higher the IV.
Options pricing must also account for a few other market realities. If the underlying happens to pay dividends, and one is payable prior to expiration, the pricing model must take that into account. Options pricing is also sensitive to interest rates; if the overall economic situation is one where interest rates are likely to move significantly in the near future, adjustments will be necessary.