Another way to look at the price of an option is to look at its intrinsic and extrinsic values. The price of an option is the sum of these two parts.
Let's talk about intrinsic value.
The intrinsic value is what the option is inherently worth. Or, in other words, the value of the option if it were exercised right now. It is also called exercise value. For instance, with corn prices being 4, the call option expiring in 3 weeks with a strike price of 3.75 has an intrinsic value of 0.25 (= 4.00 - 3.75). (If I exercise the 3.75 call option, I would be buying corn for 3.75 and can immediately sell it at 4 and profit 0.25). In another example, with corn price being 3.95, the put option expiring tomorrow with a strike price of 4.50 has an intrinsic value of 0.55 (= 4.50 - 3.95). (Notice how the time to expiration has nothing to do with an options intrinsic value).
Also note that an option can have zero intrinsic value. With oil prices being $50/barrel, a call option with the strike price of $60 has no intrinsic value (or an intrinsic value of zero). That is, why would I exercise the call option and buy a barrel of oil for $60 when I could just as well buy it for $50? Likewise, a put option with a strike lower than the underlying price would have no intrinsic value.
When an option has non-zero intrinsic value, we call that option in-the-money or ITM. So, if an option expires in the money, we would take care to exercise that option. As you probably guessed, an option with zero intrinsic value is called out-of-the-money or OTM. If an option expires out of the money, we would not exercise it.
Also slightly (un)related, if the strike price is on or near price of the underlying (i.e. underlying price is $51 and the strike price of the option under discussion is $50), we say the option is either at-the-money (ATM) or near-the-money.
A few posts ago, you saw the following graphs that represented the price of an option at the time of expiration. Since intrinsic value is the price of an option at expiration, the graph is an extremely useful tool to look at the intrinsic value of an option independent of time, volatility, or interest rate. The blue line is a call option with the strike of 15 and the orange line is a put option with a strike price of 35.