In this post, I will talk some about Jeffrey Tigay's Excursus 17, "The Name of the Feast of Booths", in his Jewish Publication Society commentary on Deuteronomy.
Leviticus 23:42-43 affirms that the Israelites are to dwell in booths during the Feast of Booths to commemorate the fact that God make the Israelites to dwell in booths right after the Exodus. According to Tigay, booths (Hebrew sukkoth) "are temporary structures made of branches and foliage that are used for shelter in various circumstances: by soldiers in the field, by herdsmen to protect their cattle, by watchmen guarding fruit trees, and particularly by grape harvesters who live in the vineyards during the grape harvest season" (page 469).
But what has baffled people about Leviticus 23:42-43 is that, elsewhere in the biblical narrative, the Israelites lived in tents, not booths, when they were in the wilderness. Rabbi Akiba said that the Israelites built both, but the problem with that suggestion is that the Israelites did not have access to branches and foliage in the wilderness "except, in small quantities, at oases" (page 469). Rashbam says that Leviticus 23:42-43 is "using 'booths' loosely for 'tents'" (page 469). But Tigay refers to another view: that the booth was not an earthly booth, but rather "God's protective cloud shielding [the Israelites] in the wilderness as a booth protects one from the elements" (page 469). We see that sort of idea in Psalm 105:39 and Isaiah 4:5-6.
Tigay says that booths were often used during the summer, "when grapes and other fruits were ripening and being harvested" (page 469). During the Feast of Booths---which is during the autumn---the Israelites dwell in booths to celebrate the ingathering "that has just been concluded" (page 469). During the Feast of Booths, they are celebrating the completed harvest with objects that they used during the harvest---booths, which they used so as to live near fruit trees or in vineyards during harvest time.
But Tigay states that Leviticus 23:42-43 historicizes the Feast of Booths by making it commemorative of Israel's experience in the wilderness, the same way that Passover and the Days of Unleavened Bread also celebrate events in Israel's history (the Exodus). And Tigay argues that the Hebrew Bible and post-biblical Judaism prefer to focus on history rather than nature. For example, in the Pentateuch, we often see a calendar that refers to months numerically and counts them from the Exodus (see Exodus 12:2), whereas, rarely, we see another calender system that names months according to the "state of nature" during that month. For example, Aviv (Exodus 13:4; Deuteronomy 16:1), another name for Nisan, means "barley", pointing to a stage in the growth of that particular grain. But, according to Tigay, the Hebrew Bible prefers to focus on history more than agriculture.