Sukkos as ingathering and unity

מצות סוכה אחר יוהכ"פ.

The mitzvah of sukkah comes after Yom Kippur.

The Sefas Emes asks why Sukkos is positioned right after Yom Kippur, and proceeds to explain the connection.

דכ' כי אם עונותיכם כו' מבדילין ביניכם לבין אלקיכם.

For it is written, "Rather, your sins have been separating between you and your God" (Yeshayahu 59:2).

Sins create a barrier (mavdilin) that divides a person from Hashem; iniquity is what causes separation.

ולכן אחר שנטהרו מעונות ניטל ההבדל.

Therefore, after they have been purified from their sins, the separation is removed.

Once Yom Kippur cleanses Yisrael of their sins, the dividing barrier falls away.

ויש עונות שמבדילין האחדות בין אחד לחבירו ז"ש ביניכם ממש.

And there are sins that divide the unity between one person and his fellow — this is the meaning of "between you" literally.

Some sins fracture the bond between fellow Jews; the word "beineichem" (between you, in the plural) hints at this divisiveness among people themselves.

ויש שמבדילין בין אדם למקום.

And there are those that divide between a person and the Omnipresent (HaMakom).

Other sins create a rift between a person and Hashem.

ובסוכות נעשה הכל אחדות אחד ונפשות בנ"י מתאחדין.

And on Sukkos everything becomes one unity, and the souls of Bnei Yisrael are joined together.

Having been cleansed on Yom Kippur, on Sukkos both barriers dissolve: the people are reunited with one another and the nefashos of Yisrael fuse into one.

זהו רומז הד' מינים שבלולב שנעשין אגודה אחת.

This is alluded to by the four species of the lulav, which are made into a single bundle (agudah achas).

Binding the four minim together symbolizes the reunification of all the different "types" of Jews into one cohesive bundle.

והסוכה שמתאחדין נפשות בנ"י לאביהם שבשמים.

And the sukkah [represents] that the souls of Bnei Yisrael are unified with their Father in Heaven.

The sukkah, which surrounds and gathers a person in, represents the rejoining of every Jew's soul with Avinu Shebashamayim — healing the rift between man and Hashem.

לכן נקרא חג האסיף:

Therefore it is called Chag HaAsif (the Festival of Ingathering).

Beyond the agricultural harvest, Sukkos is the "festival of gathering in" — gathering the Jewish people to one another and to Hashem.

Summary: Sins create two kinds of separation — between fellow Jews and between a person and Hashem. After Yom Kippur purifies these sins, Sukkos restores complete unity: the four species bound into one bundle express the reunion of all Jews, and the encompassing sukkah expresses the soul's reunion with its Father in Heaven — which is why it is called Chag HaAsif, the festival of ingathering.