The Kavana when dwelling in the Sukkah:

The reason behind the Mitzvah of Sukkah:[1] The verse[2] states that the reason Hashem commanded us to dwell in a Sukkah for seven days is in order so our future generations remember that G-d settled the Jewish people in Sukkos when he took them out of Egypt. In the words of the verse: “Lemaan Yeidu Doroseichem Ki Besukos Hoshavti Es Bnei Yisrael Behotzi Osam Meieretz Mitzrayim.” The term Sukkos in this verse refers to the clouds of glory [Ananei Hakavod] which surrounded the Jewish people for the sake of giving them shade, so they are not exposed to the heat and sun.[3] Thus, as a replica of this event, G-d commanded us to [build and then] dwell in a Sukkah that is made for the purpose of providing shade in order so we recall the miracles and wonders [done for us in the desert, in which the clouds of glory surrounded us for shade, and served as a protection from the sun]. Therefore[4], when dwelling in the Sukkah, every person must have intent to do so in order to fulfill G-d’s command to dwell in the Sukkah in commemoration of the Exodus, as explained next.

The Kavanah when dwelling in the Sukkah:[5] Every person must have in mind when dwelling in a Sukkah, that he is dwelling in it in order to fulfill G-d’s command to sit in a Sukkah in commemoration of the Exodus.[6] [Meaning, that by the Mitzvah of Sukkah, in addition to the general requirement by every Mitzvah to intend to fulfill the Mitzvah of God with its performance[7], by the Mitzvah of Sukkah one must also intend to do so for the sake or fulfilling the reason behind the mitzvah, which is to remember the exodus.[8]   Practically, upon dwelling in the Sukkah one is to think of commemorating the following matters:[9] 1) The exodus[10]; 2) The clouds of glory[11]; 3) The general miracles and wonders that Hashem performed for us.[12] It does not suffice to merely think about the exodus in passing thought, but rather the main point is for one to contemplate it.[13]]

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[1] Admur 625:1; Michaber 625:1; Tur 625; Rebbe Eliezer in Braisa Sukkah 11b

Other opinions: According to Rebbe Akiva [Sukkos ibid] we slept in actual Sukkahs, and the reason behind the holiday of Sukkas is to remember all the kindness that Hashem provides us with throughout the year, as in the desert we lived in considerable lack of wealth, not having any land or produce. Thus, in order to remind us of this, and give gratitude to G-d for all that he has provided us with, therefore we sleep outside of our homes in a Sukkah and learn to gain appreciation for all that we have. [Rashbam Sukkah ibid; P”M 625 M”Z 1 agrees with reason of Rashbam, as we rule like Rebbe Akiva versus Rebbe Eliezer]

[2] Vayikra 23:42

[3] Admur ibid and 429:4; Michaber ibid; Bach 625; Levush 625; Rashi and Ramban on Vayikra 23:43; Rebbe Eliezer in Sukkah ibid; See Birkeiy Yosef 625 in name of Toras Kohanim for opposite Girsa of opinions; See Bach and Taz 625 for different explanations of their debate

Other opinions: According to Rebbe Akiva, we slept in actual Sukkahs and not in clouds of glory. [Sukkah ibid]

[4] So is written in some prints of Admur ibid. In other prints the word says “Vichein”; See Likkutei Sichos 32:140

[5] Admur 625:1; M”A 625; Bach 625; Taz  625:1 that so applies according to Rebbe Akiva; Beis Hashoeiva Hilchos Sukkah 2; Kaf Hachaim 625:2; Likkutei Sichos 32:140, printed in Shulchan Menachem 3:313

[6] The reason: As the verse explicitly states that Hashem commanded us this Mitzvah in order “So you shall know.” Therefore, the intent is an integral part of the Mitzvah. [Implication of Admur ibid according to version of “Lechen” in Admur; Bach 625; P”M 625 A”A 1]

Other opinions regarding what to intend: Some Poskim rule that the main intent is for the clouds of glory, and not for the exodus. [Beis Yosef 625; Taz  625:1 that so applies according to Rebbe Eliezer] See Beis Hashoeiva Hilchos Sukkah 2; P”M 625 A”A 1; Likkutei Sichos 32:140; Background of Admur brought next!

Background on opinion of Admur: VeTzaruch Iyun from this wording of Admur if one is to intend on the clouds of glory as well as the exodus, or simply intending on the exodus suffices. From the fact that Admur and Michaber ibid bring the above reason of the clouds of glory it implies that it is this specific intention that one must have. Vetzaruch Iyun based on this as to why Admur and the Magen Avraham ibid wrote exodus as opposed to the clouds of glory. Perhaps, however, the intent of Admur in his wording is to hint to that one is to have all the intentions in mind, according to all opinions, as the Taz  625:1 explains that remembering the exodus is the reason according to Rebbe Akivah, while remembering the clouds of glory is the reason according to Rebbe Eliezer. Practically, the Peri Megadim 625 A”A 1 writes that it is implied from the Magen Avraham ibid that there is no need to intend for the clouds of glory, although based on the Taz ibid he concludes that it is proper to have both intentions. Accordingly, it is possible to likewise learn in Admur ibid that one is required to have both intents and he thus brought down both reasons. [So learns the Rebbe in his initial understanding in Likkutei Sichos 32:146] Nonetheless, in Likkutei Sichos 32:140 and footnote 47 the Rebbe concludes that according to Admur there is no need to intend on the clouds of glory as that is the essence of the Sukkah, and one only needs to intend on the exodus.

[7] See Admur 60:5

[8] Bach ibid

[9] See P”M 625 A”A 1, M”Z 1; Piskeiy Teshuvos 625:1 footnote 3; Likkutei Sichos 32:140; Previous footnote

[10] Admur ibid; M”A ibid; Bach ibid; Taz 625:1 that so applies according to Rebbe Akiva; Likkutei Sichos 32:140 that so is the main opinion of Admur ibid, as rules Bach

[11] Beis Yosef 625; Taz 625:1 that so applies according to Rebbe Eliezer; P”M 625 A”A 1 and M”Z 1 based on Taz ibid; Possible implication of Admur ibid who mentions this in the reason for the Mitzvah, and so learns the Rebbe in his initial understanding in Likkutei Sichos 32:146. However, in his conclusion there it is implied that according to Admur ibid there is no need to have this intent, as we would have explicitly stated this otherwise.

[12] Possible implication of Admur ibid who mentions this in the reason for the Mitzvah; See Rashbam ibid in explanation of Rebbe Akiva

[13] Igros Kodesh 4:14, Printed in Shaariey Halacha Uminhag 2:267, Shulchan Menachem 3 p. 209

[14] Bach 625; According to this opinion, if one did not have this intent on the 1^st night of Sukkos when there is an active obligation to eat in the Sukkah, he must re-eat a Kezayis of bread there!

[15] P”M 625 A”A 1; M”B 625:1; Kaf Hachaim 625:3 Implication of Rebbe in next footnote [So is implied from Rebbe that one does fulfill his obligation despite having lack of intention, and so rules the Poskim ibid.

[16] Igros Kodesh 4:14, Printed in Shaariey Halacha Uminhag 2:267, Shulchan Menachem 3 p. 209

[17] See Admur 60:5

[18] If one does not have this intent, then he does not fulfill his obligation as explained in 60:5. [There Admur brings a dispute regarding whether Mitzvos require intent and he rules like the stringent opinion.] See Biur Halacha 60:4 “Veyeish Omrim”

[19] Admur 589:9 regarding Shofar

The reason: As his original intent of his coming to Shul to fulfill his obligation is carried into his current hearing. [ibid] 

[20] Chayeh Adam Klal 68, brought in M”B 60:10

[21] Thus, if he read Shema during prayer, or ate Matzah during the Seder, or blew Shofar, or shook Lulav, he fulfills his obligation even if he did not have explicit intent as it is clearly evident that he is only doing these matters in order to do the Mitzvah. [Chayeh Adam ibid]

[22] M”B 60:10