Shalom Eliyahu,

Before the establishment of the Hebrew calendar, the Sanhedrin would be Mekadesh the Chodesh according to the testimony of two valid witnesses who saw the moon in its renewal, and then they would raise torches on top of the mountains in order to inform all the Jewish communities about when Rosh Chodesh occurred.

After the Kutim came who attempted to disrupt the method of determining the months and began to raise torches on different dates, the raising of the torches was canceled in order to avoid confusion, and the message about the beginning of the month was delivered by messengers in the months with special Mo'adim. The Mishnah in Rosh Hashanah (2:4) says that there are six months like that.

In places that were far from Jerusalem, there was a fear that the messengers would not have time to arrive by Yom Tov. Therefore, the Chachamim made a Takanah that they should make an additional day to the Yom Tov, as a "Sfeika d'Yoma," and they would observe it according to the "regular" Yom Tov laws. The additional day is called the second Yom Tov Shel Galuyos, so even if they made a mistake on the day, they would still observe the laws of the holiday in their time.

Even after the cancellation of the Kidush of the month according to the vision and the basis of the Hebrew calendar, Yom Tov Sheni is still celebrated in the same places without changing the custom, because the Chachamim were concerned for the times when Beis Din will start to be Mekadesh the Chodesh again by the seeing of the moon.

Best Regards,

Aharon Steiner