A European Option are options which are only exercisable on the expiry date of the option and are valued using the Black Scholes option pricing forumla. There are only five inputs to the classic Black Scholes model : spot price, strike price, time until expiry, interest rate, and volatility. As such European options are typically the simplest options to value The dividend or yield on the underlying asset can also be an input on some extentions of the model. In contrast American Options can be exercised at any time up until and including the expiry date of the option.
The term European is confined to describing the exercise feature of the option (ie exercisable only on the expiry date) and is does not describe the geographic region of the underlying asset. For example, a European Option can be issued on a stock of a company listed on an Asian exchange.
DerivativeOne features a free valuation tool for European and American options