(Based on a recording from Rav Ezriel Tauber zt”l, transcribed by Rabbi Eliezer Parkoff shlita)
Rosh Hashanah is the Yom HaDin (Day of Judgment). The Gemara explains to us in detail how everyone passes before Him one by one to receive his verdict. The Unesana Tokef prayer describes how everything is determined on Rosh Hashanah: who will be born, who will live, and who will die: will he live out his allotted time, or die before his time; who by water, who by fire, who by the sword.... Who will have peace, and who will be unsettled, who will have a tranquil year, and who will suffer; who will become poor, and who will become rich, etc.
These days are rightfully labeled the Days of Awe. In the Selichos on Motzei Shabbos we recite: זוחלים ורועדים מיום בואך חלים כמבכירה מעברת משאך – “We are creeping and trembling from the day of Your coming. Heavily ill from the burden of Your wrath”. We go through Rosh Hashana dreading the outcome of our trial.
Afterwards we have the 10 Days of Teshuva to repent and prepare ourselves for the Day of Atonement. Then we stand in tefillah on Yom Kippur reciting the vidui and confessing our aveiros.
Many ask that apparently the Jewish calendar is backwards. It would be more appropriate to first have the 10 Days of Repentance during the month of Elul to prepare our repentance. Then we could confess our sins and do teshuvah on Yom Kippur. After fasting and davening the whole day, we would be ready to enter Rosh Hashanah with a clean slate and receive a good verdict.
But the order isn’t that way. First we have Elul which are days of mercy (ימי רחמים ). We then have Rosh Hashanah when we don’t ask for repentance for our sins and we don’t recite vidui. The accent of Rosh Hashanah isn’t even on our getting judged. The major thrust of the tefillos is accepting Hashem as King: “reign over the entire universe in Your glory; be exalted over all the world in Your splendor... Let everything with a life’s breath in its nostrils proclaim: Hashem, the G-d of Israel, is King and His sovereignty reigns over everything.”
So now we have to delve a little deeper into the meaning of Rosh Hashanah. Elul is the month of preparation for the Yomim Nora’im. The holy seforim tell us that a hint of the meaning of Elul lies in its name: Elul is roshei teivos (an acronym): אני לדודי ודודי לי = אלול (Shir Hashirim 6:3) “I am for my beloved, and my beloved is for me.” I love Him, He loves me.
This thought raises even more questions: in order to prepare for the Days of Awe and Judgment we cite a pasuk of a love relationship?
The answer can be found in a pasuk in Nechemia.
A remnant of Klal Yisrael came back from Bavel to Eretz Yisrael. But they weren’t tzaddikim. Many of them were intermarried. They had not yet fully repented from the aveiros that had led to the destruction of the 1st Temple. As they entered their first Rosh Hashanah, they were a broken and crestfallen nation. Ezra gathered them all together in Yerushalayim and they spent the morning in tefillah and Torah study. Then Ezra proclaimed: "Go, eat delectable foods and drink sweet drinks and send portions to whoever has nothing prepared, for the day is holy to our Lord, and do not be sad, for the joy of the Lord is your strength" (Nechemia 8:10). This last phrase is mysterious. What is the meaning of “do not be sad, for the joy of the Lord is your strength”?
The standard explanation is that by outwardly enjoying the Yom Tov, your simcha will strengthen you and you will overcome your mood, and you can enjoy the Yom Tov.