Yesterday, Sunday the 16th of September, was Rosh Hashana, the first day of the New Year in the Jewish calendar. As I have mentioned before when discussing the date of the Chinese New Year, and the date of Muslim festivals, the Jewish calendar is a lunisolar calendar. This means that it follows what the Moon and the Sun are doing.
But, unlike the date of the Chinese New Year, which is always the 2nd New Moon after the Winter Solstice, the Jewish calendar works slightly differently. Although the first day of the year is the first day of the month of Tishrei, the Bible stated that Adam and Eve were created on the first day of Nisan. So, Nisan is generally taken to be the first month of the year, even though the New Year starts on the first day of the 7th month, Tishrei! The Jewish civil year starts on the first day of Tishrei, but its ecclesiastical years starts on the first day of Nisan. Because birth is associated with Spring, it is generally thought that Adam and Eve would have been created in the Spring, so the first day of Nisan needs to fall in this time of the year.
The first day of Nisan would, of course, drift in a purely lunar calendar, because there are not exactly 12 Moon cycles in a year. If this were to happen, it would not fall in the Spring and its association with the creating of Adam and Eve would be lost. The Muslim calendar does follow a strictly lunar calendar, no correction is made for what the Sun is doing.
This is the reason all Muslim festivals drift forward by 11 days each year, so e.g. Ramadan moves and can be in any season. Because the Jewish calendar’s first day is tied into something which was said to have happened in Spring (the creation of Adam and Eve), the calendar needs to correct for the drift of a purely lunar calendar.
The way the drift is corrected in the Jewish calendar is slightly different to the way it is corrected in the Chinese calendar. Instead of decreeing that Nisan is on the first or second new Moon before or after some point in the Solar cycle (like the equinox, or the solstice), what the Jewish calendar does is allows the first day of Nisan to drift forwards by 11 days each year for 2 or 3 years, then it adds an extra month of 30 days, which makes it later again by 30 days. The extra month Adar I is added in the 3rd, 6th, 8th, 11th, 14th, 17th and 19th years of the 19-year Metonic cycle (when the lunar cycle and the solar cycle almost exactly match).