A Hebrew Birthday
וַיֹּ֣אמֶר אֲלֵהֶ֗ם בֶּן־מֵאָה֩ וְעֶשְׂרִ֨ים שָׁנָ֤ה אָנֹכִי֙ הַיּ֔וֹם לֹא־אוּכַ֥ל ע֖וֹד לָצֵ֣את וְלָב֑וֹא וַֽיהֹוָה֙ אָמַ֣ר אֵלַ֔י לֹ֥א תַעֲבֹ֖ר אֶת־הַיַּרְדֵּ֥ן הַזֶּֽה׃
He said to them: I am now one hundred and twenty years old, I can no longer be active. Moreover, יהוה has said to me, “You shall not go across yonder Jordan.”
וילך משה וגו', אנכי היום. הַיּוֹם מָלאוּ יָמַי וּשְׁנוֹתַי, בְּיוֹם זֶה נוֹלַדְתִּי וּבְיוֹם זֶה אָמוּת (סוטה י"ג):
וילך משה וגו' ... אנכי היום AND MOSES WENT ... I AM [HUNDRED AND TWENTY YEARS OLD] THIS DAY — Today my days and my years become full: for on this day (the seventh of Adar; cf. Rashi on Deuteronomy 1:3) I was born and on this day I must die (Sotah 13b).

״וַיֹּאמֶר אֲלֵיהֶם בֶּן מֵאָה וְעֶשְׂרִים שָׁנָה אָנֹכִי הַיּוֹם״, שֶׁאֵין תַּלְמוּד לוֹמַר ״הַיּוֹם״, וּמָה תַּלְמוּד לוֹמַר ״הַיּוֹם״ — הַיּוֹם מָלְאוּ יָמַי וּשְׁנוֹתַי. לְלַמֶּדְךָ שֶׁהַקָּדוֹשׁ בָּרוּךְ הוּא יוֹשֵׁב וּמְמַלֵּא שְׁנוֹתֵיהֶם שֶׁל צַדִּיקִים מִיּוֹם לְיוֹם מֵחֹדֶשׁ לְחֹדֶשׁ, שֶׁנֶּאֱמַר: ״אֶת מִסְפַּר יָמֶיךָ אֲמַלֵּא״.

\“And he said to them: I am one hundred and twenty years old today” (Deuteronomy 31:2). As there is no need for the verse to state “today,” since it is clear that Moses was speaking on that day, what is the meaning when the verse states “today”? It is to teach that Moses was speaking precisely, as if to say: Today my days and years are exactly filled and completed. This comes to teach you that the Holy One, Blessed be He, sits and fills the years of the righteous from day to day and from month to month, as it is stated: “The number of your days I will fulfill” (Exodus 23:26). Similarly, the Patriarchs merited that their years be fulfilled to the day, and so they died on the same date they were born.

וַיֹּאמֶר אֲלֵיהֶם בֶּן מֵאָה וְעֶשְׂרִים שָׁנָה אָנֹכִי הַיּוֹם שֶׁאֵין תַּלְמוּד לוֹמַר הַיּוֹם הַיּוֹם מָלְאוּ יָמַי וּשְׁנוֹתַי לְלַמֶּדְךָ שֶׁהַקָּדוֹשׁ בָּרוּךְ הוּא מַשְׁלִים שְׁנוֹתֵיהֶם שֶׁל צַדִּיקִים מִיּוֹם לְיוֹם וּמֵחֹדֶשׁ לְחֹדֶשׁ דִּכְתִיב אֶת מִסְפַּר יָמֶיךָ אֲמַלֵּא
The verse relates what Moses said to the Jewish people at the end of his life: “And he said to them: I am a hundred and twenty years old this day; I can no longer go out and come in; and the Lord has said to me: You shall not go over this Jordan” (Deuteronomy 31:2). The wording is problematic, as there is no need for the verse to state the term “this day.” Moses said it in order to indicate: On this day, my days and years have been completed to be precisely one hundred and twenty, in order to teach you that the Holy One, Blessed be He, completes the years of the righteous from day to day and from month to month, as it is written: “The number of your days I will fill” (Exodus 23:26), indicating that the righteous will live out their years fully.
וּמִנַּיִן שֶׁבְּשִׁבְעָה בַּאֲדָר נוֹלַד מֹשֶׁה שֶׁנֶּאֱמַר וַיֹּאמֶר אֲלֵהֶם בֶּן מֵאָה וְעֶשְׂרִים שָׁנָה אָנֹכִי הַיּוֹם לֹא אוּכַל עוֹד לָצֵאת וְלָבוֹא שֶׁאֵין תַּלְמוּד לוֹמַר הַיּוֹם מָה תַּלְמוּד לוֹמַר הַיּוֹם מְלַמֵּד שֶׁהַקָּדוֹשׁ בָּרוּךְ הוּא יוֹשֵׁב וּמְמַלֵּא שְׁנוֹתֵיהֶם שֶׁל צַדִּיקִים מִיּוֹם לְיוֹם וּמֵחֹדֶשׁ לְחֹדֶשׁ שֶׁנֶּאֱמַר אֶת מִסְפַּר יָמֶיךָ אֲמַלֵּא
The baraita continues: And from where is it derived that Moses was born on the seventh of Adar? It is as it is stated: “And he said to them, I am one hundred and twenty years old today; I can no more go out and come in” (Deuteronomy 31:2). As there is no need for the verse to state “today,” since Moses could have said simply: I am one hundred and twenty years old. What is the meaning when the verse states “today”? One can learn from it that Moses was born on that date, i.e., he was exactly one hundred and twenty years old. This teaches that the Holy One, Blessed be He, sits and completes the years of the righteous from day to day and from month to month, as it is stated: “The number of your days I will fulfill” (Exodus 23:26).
את מספר ימיך אמלא שתחיו כמדת השמן אשר כנר אלהים, והוא הלחות השרשי בתולדה. והפך זה יקרה על הרוב שימות האדם קודם שיכלה הלחות השרשי בחלאים, יקרו מרוע בחירה או מצד המערכת והיסודות. והנה במלאת לאדם מספר ימיו יראה על הרוב בנים לבניו ויוכל ללמדם, כאמרו והודעתם לבניך ולבני בניך ויתוקן בחיי הזקנים עניני הדורות, כמו שספר שקרה בענין לוי קהת ועמרם:
את מספר ימיך אמלא, so that you will live as a result of the heavenly oil in the lamp of G’d. [the physical phenomenon perceived as sustaining life once it exists is a certain inherent source of moisture, described as celestial oil, as oil does not dry up on its own. Usually, life is cut short due to diseases caused by external causes which are not due to this vital oil having become depleted. When a person is granted a lifespan not cut short by disease caused by external causes, he will usually live long enough to pass on his aims in life to his children. This is the meaning of Deuteronomy 4,9 והודעתם לבניך ולבני בניך, “you will make them known to your children and to your grandchildren.” A prominent example of such a blessing was the fact that Levi lived long enough to pass on his heritage to Kehot, his son, and Amram his grandson. They each became leaders of their generation.
בן מאה ועשרים שנה אנכי היום ואין להתעצב על מיתתי שלא הייתי ראוי להיות עוד בטבע:
בן מאה ועשרים שנה אנכי היום, Moses mentions his age to remind the people that there is no reason to be sad that someone of his age has to die. According to any life expectancy and law of nature, he was no longer fit to go on living by natural means.

Rosh Hashanah translated literally means “new year.” The translation we often term Rosh Hashanah with is, “the beginning of the year.” I would like to retranslate Rosh Hashanah as, “the rebirth of the year, meaning, “A year of new life - a spiritual regeneration or growth.”

לְעוֹלָם יְשַׁלֵּשׁ אָדָם שְׁנוֹתָיו שְׁלִישׁ בַּמִּקְרָא שְׁלִישׁ בַּמִּשְׁנָה שְׁלִישׁ בַּתַּלְמוּד מִי יוֹדֵעַ כַּמָּה חָיֵי לָא צְרִיכָא לְיוֹמֵי
In light of this statement, the Sages said that a person should always divide his years into three parts, as follows: A third for Bible, a third for Mishna, and a third for Talmud. The Gemara asks: How can a person divide his life this way? Who knows the length of his life, so that he can calculate how long a third will be? The Gemara answers: No, it is necessary for one’s days, i.e., one should divide each day of his life in this manner.
אלא ושלשתם - מדלא כתיב ושניתם שישלישם:

He can divide his weeks into thirds studying a different area of Torah during each segment of days.

לא צריכא ליומי - פירש בקונטרס ימי השבת כלומר שני ימים מקרא ושני ימים משנה ושני ימים גמרא ולא נהירא דא"כ אכתי הוה מצי למיפרך מי ידע כמה חיי ונ"ל לפרש בכל יום ויום עצמו ישלש על כן תיקן בסדר רב עמרם גאון כמו שאנו נוהגים בכל יום קודם פסוקי דזמרה לומר מקרא ומשנה וגמרא ור"ת פי' שאנו סומכין אהא דאמרינן בסנהדרין (דף כד.) בבל בלולה במקרא במשנה ובגמרא דגמרת בבל בלול מכולם:

Each individual day should be divided into the three areas of study.

דלא ליפלוג לישני על פלגי מים א"ר תנחום בר חנילאי לעולם ישלש אדם שנותיו שליש במקרא שליש במשנה שליש בתלמוד
he will not become confused by the different versions of the same statements he hears from each teacher, as he will have no clear authoritative version from one source. The Gemara continues discussing the verse cited above: “By streams [palgei] of water” (Psalms 1:3). Rabbi Tanḥum bar Ḥanilai says: Since the root peh, lamed, gimmel can also refer to dividing, the verse is interpreted as follows: A person should always divide his years into thirds, as follows: One third for Bible, one third for Mishna and one third for Talmud.
דלא ליפלוג לישני - שלא יתחלקו הלשונות דהאי גריס שמעתא בהאי לישנא והאי גריס לה בלישנא אחרינא וחדא מילתא היא ומיהו תלמיד דגריס מתרוייהו (לישני) משתבש בגירסיה משום דמבלבל לישני:

What is the Gemara teaching us?

No one lives forever.

(ג) וְתָּא חֲזֵי, כַּד חָב אָדָם בְּאִילָנָא דְּאֲכַל מִנֵּיהּ, גְּרַם לְהַהוּא אִילָנָא דְּשָׁרֵי בֵּיהּ מוֹתָא לְכָל עָלְמָא...

When Adam sinned by eating of the tree, he brought death to the whole world...

(ט) כַּד חָב אָדָם בְּאִילָנָא דְּאָכַל מִנֵּיהּ, גָּרַם לְהַהוּא אִילָנָא, דְּשָׁרֵי בֵּיהּ מוֹתָא לְכָל עָלְמָא...

We don’t how long we will live therefore we must utilize and prioritize the time that we have here on earth. What is the best day to do that? Perhaps Rosh Hashanah, or even better, on one’s Hebrew birthday!

יום הולדת [את] פרעה. יש לי לומר יום זה תכלית שנתן ביום שנולד, ודומה לו ביום הולדת (אותם) [אותך] (יחזקאל טז ד), ונראה לי הולדת מהולדת, ורוב בני אדם מחבבים יום שהוא תשלום שנתן, שהוא כנגד אותו היום שנולד ושמחים בו ועושין בו משתה...

Most people are happy and make a seudah on the day they were born.

A birthday party made with words of Torah and praising Hashem would turn the party into a seudas mitzvah (Yabe’ah Omeir, Orach Chayim 6:29:4)

The second great miracle is that Hashem allows that same person to merit celebrating the day of his birth or birthday, a year later.

וּתְשׁוּבָה וּתְפִלָּה וּצְדָקָה מַעֲבִירִין אֶת רֽוֹעַ הַגְּזֵרָה:
Congregation followed by Chazzan:
But repentance, and prayer and charity annul the evil decree.

A person’s hebrew birthday has to a lot to do with teshuvah, tefillah and tzedakah. In what way?

(ב) וּ֝צְדָקָ֗ה תַּצִּ֥יל מִמָּֽוֶת׃

(2) But righteousness saves from death.

A person’s birthday, on a personal level, is like a second Rosh Hashanah!

R’ Menachem Schneerson zt”l, has written about understanding one’s birthday as his own personal Rosh Hashanah; one ought to say extra tehillim or specific tehillim corresponding to one’s upcoming birthday (see Iggeros Kodesh Volume 3, page 451).