There are three names for the festival which begins on the fifteenth of Tishrei:
Ḥag Ha-Sukkot, the Festival of Booths, after its primary mitzva;
The Festival of Ingathering (Ḥag Ha-asif), as it falls during the time of year when the gathering in of the harvested grain and fruit is finished;
The Festival (He-ḥag), as it is the festival par excellence. It is sometimes referred to this way without any further elaboration, as we read, “At that time Shlomo kept the Festival (He-ḥag) for seven days” (2 Divrei Ha-yamim 7:8). This is because it is the most joyous and festive of the festivals; it has the added joy of dancing at the Simḥat Beit Ha-sho’eva celebration (Tosefot Yom Tov to Rosh Ha-shana 1:2; below, section 10), and Israel would offer more sacrifices on Sukkot than on the other festivals (Ha’amek Davar to Devarim 16:13). The special joy of Sukkot will be explained below (section 8).
There are three fundamental and interrelated elements of the festival of Sukkot:
The intrinsic holiness of the days (including Shemini Atzeret), which conclude the annual cycle of festivals, and during which we rejoice and give thanks to God for the year’s crops. This sanctity is expressed in the mitzva to refrain from melekhet avoda (occupational work; see Peninei Halakha: Mo’adim 11:1) on the first and eighth days, which are holidays, and in the partial abstention on the intermediate days of Ḥol Ha-mo’ed. The sanctity of these days is also expressed in the extra sacrifices that we are commanded to offer on this festival, as described in Bamidbar (29:12-34).
The mitzva of the arba’at ha-minim (four species), which adds to the joy of gathering in the year’s produce and of the repentance and atonement achieved during the Days of Awe.
The mitzva of sukka, which gives the festival its name, so that every generation knows that God redeemed Israel from Egypt and watches over His people. The sukka also alludes to a time in the future, when God will spread His sukka of peace over us, over all of Israel, and over the entire world.
These three elements are introduced in the section of the Torah that deals with the holidays (Vayikra 23:33-44). In contrast to other festivals, which are each described as a single unit, Sukkot is described in three stages. First:
The Lord spoke to Moshe saying: Say to the Israelites: On the fifteenth day of this seventh month there shall be the Lord’s seven-day festival of Sukkot. The first day shall be a sacred occasion: you shall not work at your occupations; seven days you shall bring offerings by fire to the Lord. On the eighth day you shall observe a sacred occasion and bring an offering by fire to the Lord; it is a solemn gathering; you shall not work at your occupations. (33-38)
Mark, on the fifteenth day of the seventh month, when you have gathered in the yield of your land, you shall observe the seven-day festival of the Lord; a complete rest on the first day, and a complete rest on the eighth day. On the first day you shall take the fruit of a hadar tree, branches of palm trees, boughs of dense-leaved trees, and willows of the brook, and you shall rejoice before the Lord your God seven days. (39-40)
You shall observe it as a festival of the Lord for seven days in the year; you shall observe it in the seventh month as a law for all time, throughout the ages. You shall dwell in sukkot seven days; all citizens in Israel shall dwell in sukkot, in order that future generations may know that I made the Israelites dwell in sukkot when I brought them out of the land of Egypt, I the Lord your God. (Ibid. 41-43)