לְמַעַן֮ יֵדְע֣וּ דֹרֹֽתֵיכֶם֒ כִּ֣י בַסֻּכּ֗וֹת הוֹשַׁ֙בְתִּי֙ אֶת־בְּנֵ֣י יִשְׂרָאֵ֔ל בְּהוֹצִיאִ֥י אוֹתָ֖ם מֵאֶ֣רֶץ מִצְרָ֑יִם אֲנִ֖י יְהוָ֥ה אֱלֹהֵיכֶֽם׃
כּדי אײַערע דוֹר-דוֹרות זאָלן װיסן, אַז אין בײַדלעך האָב איך געמאַכט זיצן די קינדער פֿון ישׂראל, װען איך האָב זײ אַרױסגעוציגן פֿון לאַנד מִצרַיִם: איך בין ה׳ אײַער גאָט.
Mei HaShiloach
"You should dwell in Sukkot for seven days... Because in Sukkot I delivered Bnei Yisrael and brought them out of Egypt" –Here, after the determination of fate on Yom Kippur, the Israelites were ordered to dwell in Sukkot. The explanation of this by my master my teacher my Rabbi Yitzchak, the holy wise one, may his righteousness be blessed with life in Olam Habah, that in every place that Israel triumphs and succeeds over the nations, they then need to cleanse themselves with the mitzvah of Sukkah, like we find with Yaakov our father had triumphed over the other nations as it says, “And he built sukkahs for himself.” And moreover, after Israel triumphed over Mitzrayim, it says about their leaving “Bnei Yisrael journeyed from Rameses to Sukkot…” and it also says, “for in Sukkot I delivered Bnei Yisrael…”
Tze'enah Ure'enah
“I made the Israelite people live in booths” [23:43]. Some sages say that the Israelites also made booths in the wilderness in the way that we make them, out of wood and covered with tree branches. Therefore, we make them in the way that they made them to show the sign that the Holy One had shown to Israel in the wilderness. If you will ask, where did the Israelites get trees in the desert where they do not grow? The explanation is that merchants from foreign lands brought the Israelites everything they needed. Some sages say that the booths were clouds over Israel, and a cloud for each of the four sides.14Bahya, Leviticus, 23:43.
Rashi
כי בסכות הושבתי THAT I MADE [THE CHILDREN OF ISRAEL] ABIDE IN BOOTHS — This does not mean literally “booths” but, “the clouds of Glory" by which they were sheltered (cf. Onkelos; Sifra, Emor, Chapter 17 11; Mekhilta; Sukkah 11b).