Because options prices can be modeled mathematically with a model such as the Black-Scholes, many of the risks associated with options can also be modeled and understood. This particular feature of options actually makes them arguably less risky than other asset classes, or at least allows the risks associated with options to be understood and evaluated. Individual risks have been assigned Greek letter names, and are sometimes referred to simply as "the Greeks."
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.
Options are powerful because they can enhance an individual’s portfolio. They do this through added income, protection, and even leverage. Depending on the situation, there is usually an option scenario appropriate for an investor’s goal. A popular example would be using options as an effective hedge against a declining stock market to limit downside losses. Options can also be used to generate recurring income. Additionally, they are often used for speculative purposes such as wagering on the direction of a stock.
When buying or selling options, the investor or trader has the right to exercise that option at any point up until the expiration date - so simply buying or selling an option doesn't mean you actually have to exercise it at the buy/sell point. Because of this system, options are considered derivative securities - which means their price is derived from something else (in this case, from the value of assets like the market, securities or other underlying instruments). For this reason, options are often considered less risky than stocks (if used correctly). 
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