Options are financial instruments that give the holders certain rights that they can exercise at the time of expiration. A call option gives its owner the right to purchase an underlying asset at a specified price and at a specific time. A put option gives its owner the right to sell the underlying asset at a specified price at a specific date. 

Contrary to the futures contracts, the options contracts are based on rights and not on obligations. If the holder of an option contract chooses not to exercise the contract because there is no potential profit on this, the holder would only lose the option premium. This is not true for future contracts where the holders must liquidate the contract at expiration.

The concept of moneyness is relevant in determining the value of an option at expiration. At the time of expiration, an option may be in-the-money, out-of-the-money or at-the-money.  A call option is in-the-money when the stock price is higher than the exercise price of the option. Inversely, a call option at expiration is said to be out-of-the-money if the exercise price is greater than the stock price. 

At expiration time, a put option is in-the-money if the exercise price is greater than the stock price, and is out-of-the money if the exercise price is lower than the stock price, because selling the underlying at expiration is not profitable based on the exercise price, as the market price is higher.

Regarding the possibility of exercising the right of the option contract at any moment or at expiration, options can be classified into European and American options. The key difference between them is only about the exercise privileges associated with the options. An American option can be exercised at any time, while a European option can be exercised only at expiration. At expiration, both European and American options have exactly the same exercise rights and therefore have identical values.

You can learn more about the basics of options here.