American option expirations are the type of expiration that we would expect most stocks and ETFs to have. Index options, however (such as SPX, XSP, and NDX) have European expirations. Aside from tax advantages, the main benefit of European options (for premium sellers) is that they do not have assignment risk and merely settle cash at expiration, and yet they can still be closed at any time by the trader. The main thing to know about an American expiry is that shares (or another form of underlying security) can be assigned early. The Black-Scholes model was not meant to handle the complexity of American options and therefore it is a complexity passed down to the discretion of the trader. From the perspective of the options holder, the flexibility to exercise an option at an early date arguably makes American options more valuable than European equivalents, but this gets priced as an extra premium on American options. From the perspective of premium sellers, that same [American] flexibility is seen as a liability since it can mean random assignment and therefore sudden and unplanned portfolio imbalances. 

In contrast to American-style options, and having nothing to do with geographic location, European-style options are a type of option contract that can only be exercised at the expiration date. This is usually the style of index options, such as SPX, XSP, NDX, RUT, and DIA. Tax laws differ in every country, but it is normal to have tax advantages (Section 1256) from European options in the form of 60% of profit going toward long-term capital gains, even if open for a few seconds. There are also usually margin benefits (often in the form of a substantial buying power increase) if using short European options because there is a lack of assignment risk. For the same reasons, premium sellers love the control and [if applicable] the tax benefits of European options. Therefore, for that advantage to be worth it for European option holders, they tend to cost a bit extra. But then on the other hand, premium sellers do get paid a bit extra for that accordingly.