A European option can only be exercised at a pre-determined price (written into the option contract) on the expiry date of the option.
European options are significantly easier to value than American options. This is because American options add the complication of determining the optimal exercise time. The result is that almost all formulae for valuing options are for European options.
An important exception are American call options. For these, the optimal time to exercise is always on expiry, and, therefore, their value is the same as that of a European call with the same terms.