This coming year, 5776, will be a leap year, with an extra month of Adar. A leap year occurs every two to three years in order to ensure that Pesach always falls in the spring, as the Torah commands. Originally, there was no fixed calendar, and the leap years were declared by the Beis Din.
According to the Rambam, the Beis Din would take three factors into consideration when determining if the year should be a leap year: 1) the vernal equinox, 2) the ripening of the barley crops, and 3) the blooming of the fruit trees.
Spring or vernal equinox is the day when, because of the central position of the sun, day and night are approximately of equal length. When the vernal equinox would fall on the 16th of Nissan or later, the Beis Din would add another Adar, so that Pesach would take place after the equinox. In that case, other factors didn’t need to be considered.
When the equinox would fall before the 16th of Nissan, the Beis Din could still declare a leap year if both the barley crops were late in sprouting and the fruit trees were late in blooming. The reason for that is that barley needs to be ripe by the second day of Pesach in order to bring the korban omer and the fruit trees need to bloom in the month of Nissan.
Sometimes a leap year was declared even in the absence of those factors, such as when the roads were not suitable for travel due to the rainy season, which would prevent people from coming to Yerushalayim for Pesach on aliya l’regel. Another reason for adding an extra Adar was when the Jews living outside of Eretz Yisrael had left their homes but hadn’t been able to reach Yerushalayim in time for Pesach.
The announcement declaring a leap year would be made in the beginning of the month of Adar, stating that the following month was going to be another Adar, before the month of Nissan.
The ability to determine when to declare a leap year was called “sod ha’ibur” – the secret of the leap year. According to Pirkei d’Rabi Eliezer (chapter 8), Hashem revealed this secret to Adam Harishon, who passed it on to Chanoch, who passed it on to Noach, who passed it on to Shem, who passed it on to Avraham, who passed it on to Yitzchak, who passed it on to Yaakov, who passed it on to Yosef. During the Egyptian slavery the secret was lost, but Hashem revealed it to Moshe and Aharon before they left Egypt.
Since then, and until the destruction of the first Beis Hamikdash, the leap year was declared by the Beis Din, usually the Sanhedrin, whose judges had received semicha – ordination through an unbroken chain of rabbis going back to Moshe Rabbeinu. The Beis Din would then send a letter to all the Jewish communities, informing them of the reasons for the declaration.
During the Babylonian exile the sages of Bavel were given permission to declare a leap year. After Ezra Hasofer returned to Eretz Yisrael, the navi Yechezkel, who remained in Bavel, wanted to declare a leap year, but Hashem informed him through prophecy that the secret of the leap year had been taken away from Bavel and returned to the Jews of Eretz Yisrael.
During the period of the second Beis Hamikdash the Sanhedrin again took charge of declaring leap years. After its destruction, however, the Jews were persecuted by the Romans, and there were prolonged intervals of time when no Beis Din was able to meet and no leap years were declared. For that reason, Rabbi Akiva declared three leap years in a row while he was imprisoned by the Romans.
For three more centuries, leap years were determined by the Beis Din. However, this procedure was in danger. The Romans prohibited the rabbis from conferring semicha, under the threat of death. Hillel II, the Nasi who lived in 4th century CE, foresaw that soon there would be no one left who had the authority to declare a leap year. Hillel took action. He convened a Beis Din, composed of rabbis with semicha, and together they calculated a fixed calendar for all future generations.
Hillel’s calendar is based on a nineteen-year cycle, where the 3rd, 6th, 8th, 11th, 14th, 17th, and 19th years are leap years. This calendar is still in use today, and this coming year, 5776, is the 19th year in the cycle.