Shemini Atzeres
The Midrash says that after seven days of Succos, Hakadosh Baruch requests us to celebrate one additional day. Hashem says, פרידתכם עלי קשה, "It is hard for Me when you leave." The Imrei Emes writes that the feeling should be mutual and Bnei Yisroel should also feel that it is difficult to part from the Yomim Tovim.
According to some opinions and some siddurim, Shemini Atzeres isn't referred to as a חג (see Shulchan Aruch 668). The Rema MiPano explains that one literal translation of חג is a circle. All yomim tovim are a chag, a circle, surrounding a primary, focal point. The focal point is Shemini Atzeres. The other yomim tovim are called חג because they are like circles going around the middle point, which is Shemini Atzeres.
This idea can be likened to a chasunah. At a wedding, there is a chuppah, dancing, and a meal, but the purpose of it all is for the chasan and kallah to go home and build a life together. The Sfas Emes says that the yomim tovim represent various stages of a chasunah. For example, the schach on the succah resembles the chuppah. After the chuppah is the yichud, an even greater unity, and it occurs on Shemini Atzeres.
It states in Mishlei ליום ותשחק לבושה והדר עוז אחרון. The Vilna Gaon zt’l explains: עוז is Rosh Hashanah because Hashem judges us with His might. והדר refers to Succos, the day we take a הדר עץ פרי. And then comes Shemini Atzeres, אחרון ליום ותשחק, a day of immense happiness.
The Gemara (Taanis 7) discusses הגשמים יום גדול "How great is the day it rains!" The Avodas Yisrael zt’l explains that the Gemara refers to the greatness of Shemini Atzeres, the day we daven for rain.
The Chasam Sofer zy'a teaches that Shemini Atzeres is greater than Yom Kippur because Yom Kippur is to love Hashem through affliction (fasting, etc.). In contrast, Shemini Atzeres is to love Hashem through joy, which is a more ideal way of connection, as it states (Shir HaShirim 7:7) אהבה נעמת ומה יפית מה בתענוגים, "How beautiful it is when the love is with pleasure and joy."
The Chinuch (324) writes that we don't take the four minim on Shemini Atzeres because the four minim remind us to direct our joy (of gathering the crops) to Hashem. On Shemini Atzeres, we don't need reminders because, 'לה כולו השמיני יום, "The eighth day is solely for Hashem." The day was designated to be with Hashem. We don't need any reminders on this day.
The Yesod Yosef writes, "The custom is to take all the sifrei Torah out of the aron kodesh... Because when a father loves his son, he opens all his treasuries for him and doesn't withhold anything. Similarly, Hashem bestows upon us immense goodness."
The Zohar states, "On Hoshana Rabbah, the judgment is completed, and the blessings begin. On the following day (Shemini Atzeres), the Jewish nation celebrates with the King and receives blessings for the entire year. Only the Jewish nation is present at that celebration, and when one sits alone with the king, whatever he asks will be granted." The final words reveal the unique strength of tefillah on Shemini Atzeres. "When one sits alone with the king, whatever he asks for will be granted."
Reb Chaim Palagi zt’l teaches, "Be extremely careful with the tefillos of Shemini Atzeres to say them with immense kavanah... There is no better day and greater eis ratzon than this day when Hashem desires to hear our tefillos.... Everything depends on this day."
The Kotzker zt'l said that on Shemini Atzeres is the gzar din (the decree) for parnassah. His son, Rebbe Dovid zt'l, used to daven beyichidus (by himself). On Shemini Atzeres, the Kotzker called for him and said that on Shemini Atzeres, it is crucial to daven with a minyan because, on this day, it is decreed how much parnassah one will receive the coming year. This is hinted at in the words שמח אך והיית, which the Gemara says refers to Shemini Atzeres and whose final letters spell ך"חת, the name of the malach appointed over parnassah.
Reb Aharon Chernobyler zt’l said that benching גשם on Shemini Atzeres is mesugal for parnassah.
