There are four “New Years” mentioned in the Mishnah (Tractate Rosh Hashanah 1:1), each signifying a new beginning for different aspects of life: 1 Tishrei (Rosh Hashanah), 1 Nisan (for kings and festivals), 1 Elul (for tithes), and Tu Bishvat (for trees).
Here’s a breakdown:
1st of Tishrei – Rosh Hashana – New Year for Years
This is the most widely known Jewish New Year, marking the beginning of the Jewish calendar year and the start of the High Holy Days. On Rosh Hashanah, the calendar year changes (for example, from 5785 to 5786). It’s the beginning of the agricultural, financial, and legal year (like Sabbatical years and Jubilee years).
The Torah never refers to the first day of the seventh month as Rosh ha-Shanah. That term first appears in Ezek. 40:1. In the Torah, it is called a “day of remembrance” or “a day of sounding the shofar.” Readers may be surprised to learn that Rosh ha-Shanah begins the seventh month of the Hebrew calendar rather than the first. It commemorates the creation of the world, which traditionally is believed to have happened in the fall, the beginning of the new agricultural cycle. But the people Israel date their calendar from the Exodus, which happened in the spring (cf. Exod. 12:2 designating the month of the Exodus as the first month of Israel’s calendar).
[Etz Hayim: Torah and Commentary, pp. 727-728]
תִּשְׁרֵי (transliterated Tishrei or Tishri) is described in the Torah as the 7th month of the Hebrew year.
Timing: Early fall (September–October on the Gregorian calendar)
15th of Sh’vat – Tu BiShvat – New Year for Trees
This marks the beginning of the agricultural cycle for trees in Israel. It’s when the tithes from fruit trees were calculated. Today, it’s celebrated as an environmental and agricultural holiday, often called the “Jewish Arbor Day.”
שְׁבָט (transliterated Sh’vat or Shevat) is described in the Torah as the 11th month of the Hebrew year.
Timing: Winter (January–February on the Gregorian calendar)
1st of Nisan – New Year for Kings and Festivals
This is when the reigns of Jewish kings were counted (regardless of when they actually began ruling — it was “bumped up” to Nisan). It’s also significant for the religious calendar, as Nisan is the month of Passover and marks the Exodus from Egypt. In the Torah, Nisan is considered the first month of the year.
Timing: Spring (March–April on the Gregorian calendar)
נִיסָן (transliterated Nisan or Nissan) is described in the Torah as the 1st month of the Hebrew year.
This was the cut-off date for determining which animals had to be tithed in Temple times. Animals born before and after Elul 1 were counted separately for the tithe.
Elul (אֱלוּל) is described in the Torah as the 6th month of the Hebrew year.
Timing: Late summer (August-early September on the Gregorian calendar)
Conclusion
You may notice that the Bible speaks of Rosh Hashanah as occurring on the first day of the seventh month. The first month of the Jewish calendar is Nissan, occurring in March and April. Why, then, does the Jewish “new year” occur in Tishri, the seventh month?
Judaism has several different “new years,” a concept which may seem strange at first, but think of it this way: the American “new year” starts in January, but the new “school year” starts in September, and many businesses have “fiscal years” that start at various times of the year.
[via Rosh Hashanah – Judaism 101 (JewFAQ)]