Fluctuations in option prices can be explained by intrinsic value and extrinsic value, which is also known as time value. An option's premium is the combination of its intrinsic value and time value. Intrinsic value is the in-the-money amount of an options contract, which, for a call option, is the amount above the strike price that the stock is trading. Time value represents the added value an investor has to pay for an option above the intrinsic value. This is the extrinsic value or time value. So, the price of the option in our example can be thought of as the following:
A call option is a contract that gives the investor the right to buy a certain amount of shares (typically 100 per contract) of a certain security or commodity at a specified price over a certain amount of time. For example, a call option would allow a trader to buy a certain amount of shares of either stocks, bonds, or even other instruments like ETFs or indexes at a future time (by the expiration of the contract). 

The purchase of a call option is a long position, a bet that the underlying futures price will move higher. For example, if one expects corn futures to move higher, they might buy a corn call option. The purchase of a put option is a short position, a bet that the underlying futures price will move lower. For example, if one expects soybean futures to move lower, they might buy a soybean put option.
For example, if you believe the share price of a company currently trading for $100 is going to rise to $120 by some future date, you’d buy a call option with a strike price less than $120 (ideally a strike price no higher than $120 minus the cost of the option, so that the option remains profitable at $120). If the stock does indeed rise above the strike price, your option is in the money.
The price at which you agree to buy the underlying security via the option is called the "strike price," and the fee you pay for buying that option contract is called the "premium." When determining the strike price, you are betting that the asset (typically a stock) will go up or down in price. The price you are paying for that bet is the premium, which is a percentage of the value of that asset.