Rosh Hashanah as the day of renewal and kingship

בראש השנה צריך כל אחד לקבל מלכות שמים על כל השנה כמ"ש אמרו לפני מלכיות כו'.

On Rosh Hashanah each person must accept the kingship of Heaven (malchus Shomayim) for the entire year, as Chazal said, "Recite before Me [verses of] Malchiyos…" (Rosh Hashanah 16a, 34b).

The central avodah of Rosh Hashanah is coronating Hashem as King over oneself for the whole coming year, which is why we recite the Malchiyos verses in the davening.

וע"ז היום נאמר אשר אנכי מצוך היום.

And concerning this day it is said, "which I command you today" (Devarim, e.g. 8:11).

The Torah's recurring word "today" (hayom) alludes to Rosh Hashanah, the day on which the commandment of accepting Hashem's sovereignty is freshly placed upon us.

ובכל יום צריך להיות כחדשים והיום הוא חדש באמת.

And every day one must regard [the mitzvos] as new, and this day is genuinely new.

Although we are meant to experience the mitzvos as new every day, Rosh Hashanah is "new" in the truest sense — it is literally the renewal of the year and of Creation itself.

וע"ז נאמר היום אם בקולי תשמעו שהוא מצות שמיעת קול שופר.

And concerning this it is said, "Today, if you would but hearken to His voice" (Tehillim 95:7) — which refers to the mitzvah of hearing the sound of the shofar.

The verse "today, if you hearken to His voice" hints at the mitzvah of hearing the shofar on Rosh Hashanah — the "voice" we are called to heed on this day.

וכדאיתא בזוהר כי אם יזכו בני ישראל יהי' הגאולה בתשרי לכן אמר משיח היום אם בקולו תשמעו.

And as the Zohar states, that if Bnei Yisrael merit, the geulah (redemption) will come in Tishrei — therefore Mashiach said, "Today, if you would hearken to His voice."

The Zohar teaches that a deserving redemption would arrive in Tishrei; thus the same verse is read as Mashiach's promise that the geulah is available "today" — on Rosh Hashanah — if only Bnei Yisrael will heed Hashem's call.

וז"ש אשר יאמר היום בהר ה' יראה שביקש אברהם אע"ה להיות נזכר העקידה לבנ"י בר"ה.

And this is the meaning of "as it is said today, on the mountain Hashem will be seen" (Bereishis 22:14) — that Avraham Avinu, may he rest in peace, asked that the Akeidah be remembered for Bnei Yisrael on Rosh Hashanah.

After the Akeidah, Avraham requested that its merit be invoked on behalf of his descendants — and the word "today" in that verse points to Rosh Hashanah, the day we recall the Akeidah before Hashem.

כמ"ש ועקידת יצחק לזרעו היום ברחמים תזכור כי מאחר שיום זה נותן חיות לכל השנה הוא היום הידוע כמ"ש היום תאמצנו כו' תגדלנו כו'.

As we say, "And the binding of Yitzchak — may You remember it today with mercy for his offspring." For since this day gives vitality (chiyus) to the entire year, it is "the known day," as we say, "Today strengthen us… today make us great…"

Because Rosh Hashanah is the wellspring of life-force for the whole year, it is referred to as "the day" par excellence. Our tefillos repeatedly invoke "hayom" — "today strengthen us, today make us great" — recognizing this day as the source from which the entire year draws its chiyus.

וע"ז נאמר אני היום ילדתיך:

And concerning this it is said, "I have today begotten you" (Tehillim 2:7).

Rosh Hashanah is a day of rebirth: "today I have begotten you" expresses how, by accepting Hashem's kingship anew, Bnei Yisrael are reborn and re-created on this day that gives life to the entire year.

Summary: On Rosh Hashanah each person must accept Hashem's kingship for the whole year, the day the Torah calls "today" (hayom). It is genuinely "new" — a renewal of Creation — and through hearing the shofar ("if you would hearken to His voice") it holds the potential for redemption, which the Zohar says could come in Tishrei. Avraham asked that the merit of the Akeidah be recalled for his children on this day, for Rosh Hashanah is "the day" that channels chiyus to the entire year and on which Bnei Yisrael are reborn: "I have today begotten you."