The lunar calendar is based on the phases of the moon, which cycle from the darkness of a new moon to the brightness of a full moon 12 times each lunar year. The solar calendar is based on how long it takes the Earth to complete one orbit around the sun.
Our civil calendar, the one people in the US use, is the Gregorian calendar, which is based on the solar year. This civil calendar, used by most of the world, has abandoned any correlation between the moon cycles and the month, and has set the lengths of the months to standard 28, 30 or 31 days.
But Jews and Muslims use the lunar calendar.
The Jewish and Muslim calendar is based on three astronomical events : the rotation of the Earth on its axis (a day); the revolution of the moon around the Earth (a month); and the revolution of the Earth about the sun (a year). On average, the moon revolves around the Earth in about 29½ days. The Earth revolves around the sun in about 365¼ days, that is, about 12.4 lunar months.
The lunar month on the Jewish and Muslim calendar begins when the first sliver of moon becomes visible after the dark of the moon. In ancient times, the new month was declared when two independent, reliable witnesses reported observing the new moon. When the Sanhedrin (the leaders of that time), heard testimony from the two witnesses that they had seen the new moon, they would declare Rosh Chodesh (first of the month) and send out messengers to tell people when that month had begun.
There are approximately 365 days in the solar year. But there are 354 days in the lunar calendar, 11 days fewer than the solar calendar. Judaism and Islam treat this disparity differently.
Because many Jewish holidays are seasonal celebrations, like Sukkot, the fall harvest festival, and Passover, which takes place in the spring, the Jewish calendar inserts an extra month every three years (when the 11-day annual discrepancy between the solar and lunar calendars totals around 30 days) so that the holidays always fall in the same seasons.
The Muslim calendar, however, follows a strictly lunar schedule of a 354-day year because Islam’s major holidays are not connected to specific seasons or agricultural harvests. For Muslims there are twelve lunar months in each year. During Ramadan, the 9th lunar month, fasting starts on the first day of the month, with the sighting of the new moon. Eid El Fiter starts with the sighting of the new moon indicating the beginning of Shawal, the 10th lunar month.
As a result of these two different adaptations of the lunar calendar, Ramadan and Rosh Hashana begin on the same day only once every 33 years.
Photo: By Jessie Eastland (Own work) [CC BY-SA 3.0 (http://creativecommons.org/licenses/by-sa/3.0)%5D, via Wikimedia Commons