First of all, recall that the original Yom Kippur in Chumash was the day that Moshe came down with the second luchot and Midot Ha'rachamim. Recall as well that with the help of these midot, God had agreed to Moshe's plea that He return His shchina to Bnei Yisrael, even though He had taken it away in the aftermath of chet ha'egel/ see Shmot 33;1-8). Nonetheless, the shchina itself, even though God promised that it would return, does not return immediately, Rather - only some six months later - after Bnei Yisrael build the Mishkan (see Shmot 25:8 & Vayikra 9:1-5!).

In fact, immediately after receiving the Second Luchot, the first thing that Moshe does is gather the people together and charge them with the building of the Mishkan (note Parshat Vayakhel). Even though the shchina is returning, Bnei Yisrael must become active in this process, they must do something to 'receive' the shchina. Just like Moshe had to now carve his own second luchot ["p'sol lcha..."/ see Shmot 34:1 (in contrast to the first luchot which God Himself had carved)], in a similar manner Bnei Yisrael must now become more active and build the Mishkan.

The mitzvah to build the succah immediately after Yom Kippur may reflect this same idea. Just as Bnei Yisrael began to work on the Mishkan after (and as a result of) Yom Kippur, we also begin building our succot in which can 'meet the shchina' in a manner similar to the purpose of the Mishkan.

We can also relate this to part II of our shiur on Yom Kippur in regard to the deeper meaning of kapara.

Recall from our shiur on Yom Kippur that one aspect of "kappara" was to 'protect' man, allowing him to encounter the shchina. If indeed our "kappara" on Yom Kippur was successful, then we should now be ready to encounter the shchina. Considering that our sitting under the "schach" of the succah symbolizes our sitting under the 'clouds of God's glory' in the desert ["Succot k'neged annanei ha'kavod"/ Succah 11b], then Yom Kippur could actually be considered a preparation for Succot! To enable us to 'dwell' together with the shchina in our succah, we must first complete the process of "kappara" on Yom Kippur.

This thematic connection can help us understand many other halachot and customs of Succot.

For example, the gemara in Succah 5b learns the minimum height of the succah - 10 "tephachim" - from the height of the kaporet! [Recall last week's shiur which discussed the significance of the kaporet in relation to the shchina/ see also complete sugya in Mesechet Succah beginning at the bottom of 4b.]

In fact, the same shoresh as "schach" is found in the pasuk which describes the keruvim on the kaporet: "v'hayu ha'keruvim... soch'chim b'kanfeyhem al ha'kaporet ..." (see Shmot 25:20).

This pasuk clearly shows how the "schach" of our succah reflects our dwelling under the shchina.