As with the holidays Shavuot and Sukkot, Jews living outside of the land of Israel celebrate an additional festival day, not Biblically-mandated, during which no creative work can be performed.
In antiquity, the Hebrew calendar relied from month to month on witnesses viewing the new moon and testifying before the Sanhedrin to its appearance. With the dispersal of the Jewish people around the world, those living outside the Land of Israel could not always be informed in time to observe holidays on the correct days, so they observed holidays by counting from the previous months’ calendars, adding an extra day to be certain of fulfilling the relevant Biblical commandments.
When Patriarch Hillel II formalized the perpetual calendar in the fourth century CE, the second day of festivals was permanently enacted for those choosing to live outside the land of Israel, as a means of increasing Jewish awareness that remaining in the Diaspora is a conscious decision that runs counter to Jewish destiny.
Rosh HaShana, the Jewish New Year, falls on the first day of the month of Tishrei, and the moon's status can never be checked in time to determine the holiday’s observance. Therefore, the date is determined based on the previous month's schedule and is observed for two days even in Israel.