The Midrash says that after the seven days of Succos, Hakadosh Baruch Hu says, פרידתכם עלי קשה, "It is hard for Me your departure," and Hashem asks us to stay one more day.
The question is that after Shemini Atzeres passes, it will also be hard for Hashem when we leave. So what is accomplished by staying one more day? Inevitably, there will be a moment when it is hard for Hashem, keviyachol, when we leave!
It is repeated that the Yismach Yisrael zt'l told the following mashal to answer the question:
There was a king who had a son, and they both loved each other immensely. When the son got married, he lived far away from the king, and the king and the son didn't stop yearning for one another. One day, the father, the king, came to visit. The son was very happy all the days of the visit. When it was time for the king to return to his homeland, the son came to his father and expressed his disappointment that the king will be leaving him. The father said, "I have a solution for you. Build a home for me, near where you live, and I will remain here with you."
Similarly, when Succos is about to pass, Hakadosh Baruch Hu says to Bnei Yisrael, פרידתכם עלי קשה, it is hard for Me when we depart. It is hard for both of us. However, there is a solution. Build a mishkan for me, and I will dwell with you, always."
Even in our times, when we don’t have a Mishkan, make your homes a Mishkan, a place for the Shechinah, and Hashem will remain with us the entire year.
But the person says, "But how can I possibly make a place that will be fitting for You? I am a human being, imperfect, what can I do to make a place for You?" Hashem replies, עכבו עמי יום אחד, "Stay with me for one day." This means to take upon yourself a small kabalah. Take something along with you for my sake, something small that you can keep. Hashem isn't asking for a lot. Do something small, but do it for Me, and I will dwell together with you the entire year.
Throughout succos, we bring many korbanos, but on Shemini Atzeres, we bring, פר אחד איל אחד, far fewer korbanos, just a single פר and a single איל. The Avnei Nezer explains that this is to tell us that something small is also sufficient, and Hashem will remain with us, and He will rejoice with us. This small kabbalah will maintain the light of the yomim tovim for us, throughout the year.
There is a tefillah written to be said when one leaves the succah. In this tefillah, it states, ובזכות צאתי מביתי החוצה ודרך מצותיך ארוצה יחשב לי כאילו הרחקתי נדוד, "In the merit that I left my home and went outside to perform the mitzvah of sitting in succah, may it be counted as though I went to galus." There is a certain amount of discomfort, having to leave the house to eat in the succah. We say in this prayer that if it was decreed galus, exile, on a person (or on a community, etc.) chalilah, let the galus to the succah be considered like we were already in galus, and that we already received our punishment.
The question is that galus is extremely painful. It is a far greater punishment than simply picking oneself up and eating in a succah for seven days. How can this small discomfort take the place of galus?
The Yeitav Lev (first night of Succos, 5) answers this question. He explains that in Hashem's eyes, small things are considered and viewed to be very significant and great. The small discomfort of galus to the succah, in Hashem's eyes, is viewed and considered like the person went to galus and he had already received this punishment.
We quote, "It states (Bereishis 24:1) וה' ברך את אברהם בכל, 'Hashem blessed Avraham with בכל, everything' and בכל, everything means כל דהו, anything, even a drop. The Gemara (Yoma 74a) says that כל חלב means even a drop of chelev, forbidden fats, is also forbidden. As Rashi writes, אפילו כל שהוא משמע, the word כל implies that even a tiny drop is forbidden. Therefore, when it states וה' ברך את אברהם בכל, 'Hashem blessed Avraham with בכל, everything' this means that Avraham, and also the Jewish nation, receive reward even for a כל דהו, a drop of a good deed. That, too, will make a great imprint in heaven.
"As the Chovas HaLevavos (Cheshbon HaNefesh 5) writes, 'It shouldn’t be small in your eyes anything you do for Hashem, even a word, and even a look, because the little that you do is massive for Him (כי המעט ממך אצלו רב). The same is with aveiros. The best example of this is the sun. When it moves an amah on earth, it moved vast distances in heaven'.
"Therefore, we request that going out of the house should be like going to galus. This is because in heaven, this small deed is seen far greater than it appears to us, and it makes a great imprint."
There is a wonderful vort from Reb Moshe Leib Sassover zt'l. On yom tov, we say אתה בחרתנו, "You chose us from all nations... You love and You desire us..." Immediately after yom tov passes, we say in Shemonah Esrei אתה חוננתנו..., "You give us wisdom..." (This is the Havdalah we say in Shemonah Esrei.) Rebbe Moshe Leib Sassover said, "It is the same אתה, 'You' of אתה בחרתנו, as the אתה, 'You' of אתה חוננתנו. Hashem remains the same Hashem. When it is yom tov, and when it is weekdays, we are associating with the same Hashem yisbarach. Therefore, even after the yom tov passes, don't despair, don't think that we lost our connection with Hashem, because it is the same אתה. We can still connect with Hashem with our good deeds, with our mitzvos, etc. And as we are explaining, the kabalos tovos will grant us an aspect of the yomim tovim even after the yomim tovim pass.
