Nisan-years is an ancient calendar system used around Mesopotamia. Its area of usage covers Elam, Persia, Media, Syria and Israel/Judea. Its beginning was from prehistorical era. Ever since Mesopotamia had historical writings, even before the Old Babylonian Empire of Hammurabi, its calendar used the Nisan-years.
Nisan-years is often called the Jewish Religious Calendar, in contrast to Tishri-years, which is often called the Jewish Civil Calendar.
Nisan-years belongs to the Lunisolar calendar system, in which the lunar years and the solar years are synchronized by adding in an intercalary month in a leap year. Three ancient civilizations (Babylonia, China, and Israel) knew that by adding in seven intercalary months in nineteen years (called a Small Mahzor in the Jewish Talmudic Calendar, and the Metonic Cycle in non-Jewish context), the solar and the lunar years are basically synchronized. Since a tropical year is 365.2422 days, and a synodic month is averaged 29.53059 days, in nineteen years the solar and the lunar calendars will only differ by about two hours, or 1 part in 80,000.
Nisan-years begins from the Spring season. Technically, its New Years Day is the day after the New Moon closest to (within fifteen days before or after) the Vernal Equinox (Spring Equinox, when the day and the night is of equal length, set at March 21 in the Gregorian Calendar). It begins the first month, named Nisanu/Nisan/Abib. The month of Nisan is important since it begins the Spring Feasts of Israel.
The observation of the New Moon may be influenced by the weather condition, so the Rosh Chodesh may be delayed for one or two days. But over all the errors cancel each other, and the calendar system remains accurate.
The intercalary month could be a second Sixth Month (Ululu II), as often practiced in Mesopatamia, or a second Twelfth Month (Adar II, Adar Sheni, or ve-Adar) as consistently practices in Israel.
The way to determine whether or not an intercalary month should be added was by agricultural observation in Israel. If by the end of a Nisan-year, barley did not grow spikes (called Abib in the Canaanite language, e.g. Tel-Aviv is the "Hill of the Barley Spikes"), the season is too cold, and an intercalary month should be added as the Second Adar, so that barley can be harvested in the month of Nisan. Jewish tradition fixed Nisan 16, the second day after Passover (Nisan 15), as the wave offering or omer offering in Israel, when a portion of the harvested barley is dedicated to God as a Thanksgiving. The Torah, however, fixed it on the first day after the Shabbat (Leviticus 23:9-14). It can be shown that in 1446 B.C., thought by some to be the date of the Exodus, Nisan 16 happened to be a Sunday.
It seems that Israel learned of the Nisan-years calendar system by Abraham, who came out of Ur of Chaldees, and used it consistently through the time of Moses and David. However, since David became the king of Judah (the southern two tribes) before he became the king of Israel (the norther ten tribes), and the day of ordination seemed to be Tishri 1, the first day of the seventh month, later the southern kingdom Judah used another calendar system, the Tishri-years. The tradition was still kept by the modern Jews, and they extended it to the time of creation.