The Gemara (Sukkah 53a) states that at the Simchas Beis HaShoavah, chachamim juggled with אור של אבוקות, "torches of light". They threw the "torches of light" from one hand to the other, and the light of the torches shone to all sides. We can explain, b'derech remez, that this hints to us that the light of the yom tov should shine to the entire year.
Succos has past, but as chasidim say, "It didn't pass, it went in. It became part of us. The lessons of succos, its holiness, and the brachos of the yom tov remain with us throughout the year."
The Mishnah (see Yoma ch.6) states, וסוכה הרי לו מזון הרי לו מים אומרים סוכה כל על, "At every succah that he came to, people told him, 'There is food here. There is water here.'"
Rebbe Yisrael (the Yanuka) of Stolin zt'l said that hinted in these words is that וסוכה סוכה כל על, from every year Succos, until the coming Succos, מים הרי מזון הרי לו אומרים, he receives bounty of parnassah. The mitzvos of Succos brings us a shefa of food and drink for the entire year, until next year Succos.
We daven on Succos, והשיאנו ה' אלקינו, which means that Hashem should load onto us the kedushah of the yom tov, more than we are able to carry on our own (Abudurham on Pesach). The Abudurham also explains that והשיאנו means fire (as in Rosh Hashanah 22b, משואות משיאין). We request והשיאנו ה' אלקינו את ברכת מועדיך that Hashem should enlighten us with the light of the yomim tovim.
It states (Shemos 34:22) וחג האסיף תקופת השנה, and the Sfas Emes (שמיני ה"ד ח"תרל) says that this means Succos which is תקופת השנה, the strength for the entire year. The year's existence, and all the year's bounty, comes from the Yom Tov Succos.
