The Hebrew calendar is the annual calendar used in Judaism. Like the Chinese calendar, it is also a lunisolar calendar, based upon both lunar months and a solar cycle (which defines its years). This is in contrast to the Gregorian calendar, which is based solely upon a solar cycle, or the Islamic calendar, which is purely lunar.
Jews use this calendar to determine when the new Hebrew months start; this calendar determines the Jewish holidays, which Torah portions to read, Jahrzeits, and which set of Psalms should be read each day.
Jews have been using a lunisolar calendar since Biblical times, but originally referred to the months by number rather than name. During the Babylonian exile, they adopted Babylonian names for the months. Some sects, such as the Essenes, used a solar calendar.
The beginning of each Hebrew year used to be decided by observing the growth of barley, and the beginning of each lunar month used to be decided by observing the moon (in case of cloudy skies, by guessing); the latter method is still in use by a minority of Muslim nations even today, for the Islamic calendar. The beginning of each Hebrew month had been decided in Israel and the information was transfered by torches to the main diaspora areas in Babylonia (now Iraq) and Egypt.
The observation-independent Hebrew calendar described hereafter was set in Babylonia sometime in the 4th century. The change was probably performed by a council of sages headed by Shmuel hakatan.