The term "Second Day of Yom Tov" (יום טוב שני) refers to the additional day of Jewish holiday observance outside of Israel, known as the Diaspora. This practice originates from the time when the Jewish calendar was determined by the sighting of the new moon. In ancient times, messengers were sent from Jerusalem to inform distant communities of the new moon's sighting, which signified the start of the holiday. However, due to the distance and difficulties in communication, communities outside of Israel could not be sure when the holiday actually began, so they observed an extra day to ensure they did not miss the proper date.
Today, even though the calendar is fixed and the exact dates are known in advance, the tradition of observing an extra day in the Diaspora continues. This applies to holidays such as Passover, Shavuot, Sukkot, and Shemini Atzeret. In Israel, most holidays are observed for only one day, reflecting the original biblical commandment.