The Jewish Calendar and Holidays (incl. Sabbath): The Jewish Calendar: Keeping Two Days of a Holiday:
Why do we keep many of the holidays for two days, when according to the Torah they are only one day?
Before the time of Hillel II, when the months were still proclaimed by the Sanhedrin on the basis of the testimony of witnesses, it was necessary to notify those who lived far away from Jerusalem so they would know when to observe the holidays. At first this was done using signal fires, but when this became impractical, messengers were used. This meant that in places which the messengers could not reach in time, it was necessary to observe a one-day holiday for two days, since it was not certain whether the previous month had ended after 29 or 30 days. Originally, in a place which the messengers could
reach in time, the holiday was observed only for one day. But since even the system of messengers was not always reliable, it become customary to keep all the holidays for two days everywhere outside Eretz Yisroel.
Rosh-Ha-Shanah presents a special problem because it occurs on the first of the month. There were times when the new moon was not visible in Jerusalem, and the witnesses had to come to Jerusalem from elsewhere. Occasionally they could not arrive until the afternoon, after the weekday sacrifices had already been offered and it was too late to offer the Rosh Chodesh and Rosh Ha-Shanah sacrifices. To avoid this situation, it became customary to celebrate Rosh Ha-Shanah for two days even in Eretz Yisroel.
We still do these things even now that we have a definite calendar because our use of that calendar is not permanent; when
the Sanhedrin is reestablished we will go back to the old system.
When Rosh-Ha-Shanah was celebrated for only one day, the Temple and the Sanhedrin were still in existence. In the Temple they blew the shofar even on Shabbos because Rabbinical Shabbos prohibitions do not apply in the Temple. When the Temple was destroyed, R. Yochanan b. Zakkai ruled that it was permissible to blow the shofar on Shabbos at the place where the Sanhedrin met.
In Rosh Ha-Shanah 21a we are told that Rava used to fast for two days
on Yom Kippur, "and once he was found to be right" (i.e., he found
that the new moon of Tishrei was in fact a day late that year). See
also the following story about R. Nachman, who once found out just
before the end of Yom Kippur that the new moon of Tishrei had been
a day late, so that he would have to fast another day. However, this
practice was never widely adopted because of the difficulty of
fasting for two days. Since the dates of Yom Kippur and Sukkos
were in fact not certain, Sukkos was still celebrated for two
days even though Yom Kippur was kept for only one day.
Maimonides (Kiddush ha-Chodesh 3:12) says that although there is no
doubt about when Shavuos is, since it's the 50th day of the Omer, we
keep it for two days so as not to distinguish between it and the other
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