The Torah clearly states that the Yom Tov of Sukkas comes to commemorate the “sitting in the Sukka” experience that Bnei Yisroel experienced when they left Mitzrayim.

לְמַעַן יֵדְעוּ דֹרֹתֵיכֶם כִּי בַסֻּכּוֹת הוֹשַׁבְתִּי אֶת בְּנֵי יִשְׂרָאֵל בְּהוֹצִיאִי אוֹתָם מֵאֶרֶץ מִצְרָיִם….

Loosely translated, “for your generations shall know that I placed the Jewish people in booths when I took them out of Mitzrayem”.

The obvious question is, if we are commemorating an event connected with Yetzias Mitzrayem shouldn't we be doing it during the month of Nissan when Bnei Yisroel left Mitzrayem? 

Shouldn't we be eating Matzah in the sukkah?

The Aruch Hashulchan suggests a very practical approach to this difficulty: if we would celebrate sukkas during the month of  Nissan it would look like we are leaving our homes for the pleasant outdoors weather after a long cold winter. In fact that is the way of the world, at the end of  a long and cold winter after months of beig cooped up in their homes people head outdoors to enjoy the warm springy weather. 

Therefore we celebrate sukkas at the end of the summer  showing that this is not to take advantage of the beautiful weather, rather it's a mitzvah and we are doing it leshem shomayim. 

The Aruch Hashulchan offers another deep and fundamental approach to this question.

After the sin of the golden calf Klall Yisroel felt like it would never be the same again. The sin being so severe and in such close proximity to Matan Torah left Kllal Yisroel feeling that Hahsem would never dwell  amongst them as was the case before the sin of the golden calf.

 Moshe Rabbeinu spent an additional forty days in Shomayem and at the end-  on erev yom Kippur returned with a second luchos. Kllal Yisroel merited to  receive a mechillah on Yom Kippur and following day received the shocking and euphoric news- the building of the Mishkan.

Hashem commands Moshe to build a Mishkan, a dwelling place for his shechinah amongst Bnei Yisroel. Despite the terrible sin of the golden calf,  Hahsem was telling Bnei Yisroel let's move on, I still love you and will still dwell amongst you.

This theme, says the Aruch Hashulchan, repeats itself again every year. When yom kippur comes around we feel broken and down  over all the sins we committed during the past year. Yes we do Teshuvah, yes we fast, but we tend to feel like we lost Hashems presence amongst us.

 Then comes the Yom Tov of Sukkas and Hashem command us to build a Sukkah, a dwelling place where the shechinah will rest, a place where we will jointly spend the next seven days with the shechinah. 

Hashm is telling us that despite the past, he still loves us and wishes to dwell amongst us.

This fundamental idea expresses Hashems un-ending love to us, his children.

This idea is specifically expressed during sukkas since it falls out immediately after Yom kippur.