The first Mishnah of the Talmudic tractate Rosh Hashanah states that, according to Jewish tradition, there are four starting dates throughout the year:
The first of Nissan is designated as the beginning of the year for the holidays, as well as the beginning of the counting of the years of the reign of the Jewish king.
The first of Elul is the beginning of the year for separating tenths from the offspring of livestock.
The first of Tishrei is the beginning of the general New Year, for counting the seven-year cycle, separating tenths from garden vegetables, and so on.
The 15th of Shevat is the beginning of the year for fruit: fruits that set after this date are considered part of the following year's harvest. This date has practical significance, for example, for separating tenths ("maasrot") from the fruit harvest.