A European option can be exercised only on the maturity date, while an American option can be exercised any time before or on its maturity date. Since an American option could be held until it matures, its price (option premium) should be higher than or equal to its European counterparty.
An important difference is that for a European option, we have a closed-form solution, that is, the Black-Scholes-Merton option model. However, we don't have a closed-form solution for an American option. Fortunately, we have several ways to price an American option. Later in the chapter, we will show how to use the binomial tree method, also called the CRR method, to price an American option.