The word “atzeret” derives from “atzara,” a gathering, for on this day, we gather together to bid farewell to the annual holiday cycle. This cycle begins with Pesaḥ, when we left Egypt, continues to Shavu’ot, when we were given the Torah, goes on to Rosh Ha-shana and Yom Kippur, times of remembrance, repentance, and atonement, and culminates with Sukkot, the Festival of Ingathering, when we gather in all the physical and spiritual fruits of the year and rejoice in them, thus spreading joy and blessing throughout the world. On Shemini Atzeret, which wraps everything up, we have a farewell get-together. “This can be compared to a king who invited his children to a party that was scheduled for a certain amount of time. When the time for departure arrived, he said, ‘My children, please stay with me for one more day. Saying goodbye is hard for me” (Rashi on Vayikra 23:36).
From this perspective, it is appropriate to be happier on Shemini Atzeret than on any other holiday. It is on this day, which concludes the yearly cycle of uplifting holidays, that we reach the pinnacle of closeness and connection to God. The joy we experience on Shemini Atzeret does not hinge on a specific mitzva, such as the sukka or four species, but stems from the very fact that we are God’s children and people. Thus, the Vilna Gaon says that the mitzva is to rejoice in God exclusively, as it is written, “You shall have nothing but joy” (Devarim 16:15). It is told that the Vilna Gaon rejoiced greatly on Sukkot and was even more joyful on Shemini Atzeret, because, according to esoteric teachings of the Torah, it is the happiest day of all (Ma’aseh Rav §233).
In this festive farewell get-together, when we draw especially close to God, He gave us the opportunity to permanently conserve and preserve in our souls forever all the illumination that we absorbed over the previous year. This makes it possible for us to continue to ascend in the upcoming year.
There is another holiday that the Torah calls an atzeret, namely the seventh day of Pesaḥ: “You shall hold a joyous gathering (atzeret) for the Lord your God on the seventh day” (Devarim 16:8). It is described as an atzeret for God because all the light we gather and absorb during Pesaḥ we give back to God to guard it for us, as we are not yet on the level to permanently store it within us. But six months later on Shemini Atzeret, after completing all the year’s festivals, we have reached a point where we can store within ourselves, forever, all the light and goodness that we absorbed during the year. Thus, it is written: “On the eighth day you shall hold a joyous gathering (atzeret) for yourselves.” (See Peninei Halakha: Moadim 13:6 for why Shavu’ot is also called Atzeret.)
The eighth day is fitting for this celebration, as this world, the natural world, is linked with the number seven. It was created in seven days, and everything in it is temporary and finite. In order to store all of the goodness and divine illumination that manifests in it, we must sanctify ourselves and ascend to a level beyond nature and time, a level that is linked to the number eight. The power of this level that is beyond nature makes it possible to improve the world. We are similarly commanded to perform a brit mila, which improves upon nature, on the eighth day, for the covenant is eternal, beyond nature and time. God also gave us the eternal Torah on an “eighth day” of sorts – the day after we finished counting seven weeks of seven days. For this reason, it is appropriate to associate Simḥat Torah with Shemini Atzeret, the holiday correlated with the number eight (Maharal, Tiferet Yisrael ch. 2).