A longer expiration is also useful because the option can retain time value, even if the stock trades below the strike price. An option’s time value decays as expiration approaches, and options buyers don’t want to watch their purchased options decline in value, potentially expiring worthless if the stock finishes below the strike price. If a trade has gone against them, they can usually still sell any time value remaining on the option — and this is more likely if the option contract is longer.

Options are contracts giving the owner the right to buy or sell an asset at a fixed price (called the “strike price”) for a specific period of time. That period of time could be as short as a day or as long as a couple of years, depending on the option. The seller of the option contract has the obligation to take the opposite side of the trade if and when the owner exercises the right to buy or sell the asset. For more information, check out the Ally Invest Options Playbook here: https://www.optionsplaybook.com/
Another example involves buying a long call option for a $2 premium (so for the 100 shares per contract, that would equal $200 for the whole contract). You buy an option for 100 shares of Oracle (ORCL) for a strike price of $40 per share which expires in two months, expecting stock to go to $50 by that time. You've spent $200 on the contract (the $2 premium times 100 shares for the contract). When the stock price hits $50 as you bet it would, your call option to buy at $40 per share will be $10 "in the money" (the contract is now worth $1,000, since you have 100 shares of the stock) - since the difference between 40 and 50 is 10. At this point, you can exercise your call option and buy the stock at $40 per share instead of the $50 it is now worth - making your $200 original contract now worth $1,000 - which is an $800 profit and a 400% return. 
American options can be exercised at any time between the date of purchase and the expiration date. European options are different from American options in that they can only be exercised at the end of their lives on their expiration date. The distinction between American and European options has nothing to do with geography, only with early exercise. Many options on stock indexes are of the European type. Because the right to exercise early has some value, an American option typically carries a higher premium than an otherwise identical European option. This is because the early exercise feature is desirable and commands a premium.
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).