Guide to the Jewish Year
or to Lazer's
Talmud Torah
The following is based on the Shulchan Aruch HaRav (siman 500). (This is a halachic work based on the Shulchan Aruch and is widely acknowledged as authoritative.)
This isn't a translation, just a summation of the relevant issues.
When the Sanhedrin was extant the months were set according to testimony given by witnesses who had seen the new moon. If for whatever reason witnesses did not come on the expected day then the month began a day later (even without witnesses because a month is never more than 30 days long). The fact that the new moon HAD been present was not relevant since the month had to be declared by the Sanhedrin and the Sanhedrin was unable to do so (on the 30th day of the preceding month) without witnesses.
Thus, all Jews were dependent on the Sanhedrin to know when the various Yomim Tovim would take place. Immediately after the Sanhedrin declared a new month messengers would depart from Jerusalem to inform the rest of the country of the exact date of the new month so that they would know when to celebrate the Yomim Tovim. For example, Pesach begins on the fifteenth of Nisan. The messengers would arrive in the outlying districts and inform them about when the new month began so that they would know when Pesach began.
But what if a community was more than fifteen days of travel away from Jerusalem. They would have no way of knowing when the Yom Tov would begin. It was therefore necessary for them to keep two days of Yom Tov to avoid the possibility of violating the true one. This is called Yom Tov sheini shel galiyos.
On Rosh HaShana this problem was compounded. Since Rosh HaShana was the first day of the month, immediately upon the Sanhedrin's declaration it would be Yom Tov (actually earlier because of the doubt). It would therefore be prohibited for the messengers to leave the city limits (techum) of Jerusalem. Thus no one outside of Jerusalem would know when the Yom Tov began. It was therefore necessary for all residents of Israel as well to keep two days of Rosh HaShana.
Today we keep this practice (both yom tov sheini shel galiyus and two days of Rosh HaShana) because of "minhag avoseinu" (the custom of our forefathers) even though we no longer have the Sanhedrin and instead must rely on astronomical calculations.
© Eliezer C. Abrahamson