The first of Nisan is the new year for kings and for festivals. The first of Elul is the new year for the tithe of beasts. Rabbi Elazar and Rabbi Shimon say: the first of Tishri. The first of Tishri is the new year for years, for shmitta and jubilee years, for planting and for [tithe of] vegetables. The first of Shevat is the new year for trees, according to the words of Bet Shammai. Bet Hillel says: on the fifteenth of that month.
ויהי בארבעים שנה בעשתי עשר חדש בר"ח שבט הקהיל את העם ואמר להם הגיע זמן מותי ואם יש בכם מי ששמע הלכה ושכחה יבא וישאלני ואבאר אותה וכל מי שנסתפקה עליו שאלה יבא ואפרשנה לו כמו שנאמר (דברים א) הואיל משה באר את התורה הזאת לאמר.
Shevat https://www.ou.org/holidays/months/month-shevat/
On the first of the month, Moshe, inspired by prophecy from G-d, began to recite the words of the Book of Devarim to Israel. “On the other side of the Jordan, in the land of Moab, Moshe began explaining this law, saying…” (Devarim 1).... He reviewed many of the Laws that had been taught at Sinai and at the “Ohel Moed,” the “Tent of Meeting,” the gathering place of the Jewish People around the Mishkan, where they had come to learn Torah from Moshe. The Book of Devarim is called “Mishne Torah,” “Review of Torah,” for this reason. He also taught them many additional laws at that time....
For thirty-seven days, Moshe spoke these words to all Israel. He began the first of Shevat and ended the seventh of Adar.
Because the period of transmission of the Book of Devarim was this thirty-seven day interval, all the days from the first of Shevat until the seventh of Adar are especially well suited for renewed inspiration in the study of Torah and the doing of Mitzvot.
Lubavicher Rebbe, Sicha Rosh Chodesh Shevat https://www.chabad.org/therebbe/article_cdo/aid/2539043/jewish/Rosh-Chodesh-Shevat-5742-1982.htm
1. Torah bids us to begin with a word of royalty, and our Sages say that the (true) kings are the Rabbis. Hence royalty is associated with Torah, and it is thus fitting that this farbrengenbegin with the portions of Chumash, Tehillim and Tanya (Chitas) said daily. This is especially appropriate since this farbrengen is associated with the completion of the writing of the Sefer Torah.1
The Baal Shem Tov taught that everything a Jew encounters can provide a lesson for his service to G‑d. Certainly then, every day has a unique lesson special for that day; and that lesson comes from the Torah which is peculiar to it. This is consonant with the Alter Rebbe’s dictum that we must ‘live with the times,’ meaning to live according to the lessons derived from the daily portion of the weekly parshah — and likewise with the daily portion of Tehillim and Tanya. For in addition to learning these daily portions, there are also lessons to be derived from them in our service to G‑d.
There is a central theme in today’s portions of Chumash, Tehillim and Tanya, associated with today being Rosh Chodesh Shevat, and also marking the completion of the Sefer Torah. That central theme is the emphasis on unity of all Jews. On Rosh Chodesh Shevat, Moshe Rabbeinu began to teach the Jews the book of Devorim — “These are the words which Moshe spoke to Israel.” Moshe spoke to all Jews, to all the different categories — the idea of unity among Jews. This is also emphasized in today’s portions of Chitas
Rosh Chodesh Shevat – a brief meditation on the garden of prayer - Todd Berman
https://blogs.timesofisrael.com/rosh-chodesh-shevat-a-brief-meditation-on-the-garden-of-prayer/
The first of Shevat is the new year for trees, according to the words of Bet Shammai. Bet Hillel says: on the fifteenth of that month.”
According to Beit Shammai, today is the day we should give the world’s flora its due.
Rebbi Nachman relates this to the act of prayer:
Every single word is an entire world. When a person stands up to pray and recites the words of the prayers, he is gathering beautiful buds and flowers and blossoms, like someone walking in a field picking lovely blossoms and flowers one at a time, until he makes a bouquet. After that, he picks more, one by one, making another bouquet, and joins them together. So he goes on, picking and gathering more and more lovely bouquets.
This is likewise true of prayer: a person goes from letter to letter until several letters are joined together and form a single word. He does the same for a second word. Then the two words are joined, and he goes on, gathering more until he completes a single blessing. After that, he goes on gathering more and more—from Avot to Gevurot, and from Gevurot to Kedushot [parts of the Amida prayer]. So he goes on, further and further. Who can extol the magnificent splendor of the gleanings and gatherings that a person makes through the words of the prayers?
And when speech emerges, it emerges from the soul, as it is written (Genesis 2:7), “thus man became a living soul”—which the Targum renders as: “he became a speaking spirit.” The utterance emerges and is heard by his ears, as our Sages, of blessed memory, said: Let your ears hear what you are bringing forth from your mouth (Berakhot 15a). (Likutei Moharan 65)