After the Feast of Sukkot, an extra day is added known as the "Eighth Day of Assembly". It is an extra day of abiding with the Lord - alone...us with HIM.
Eight is the number for new beginnings.
Atzeret means "Abiding".
Jesus said, "Whoever abides (Atzeret) in me and I in him, he it is that bears much fruit, for apart from me you can do nothing."
According to the Zohar, it is on this 8th day, Shemini Atzeret, that the heathens/gentiles complete and terminate their blessings and abide in judgment. But on this day, we end our judgments and abide in blessings. We take delight with the King and take blessings from Him for the WHOLE YEAR. It is on this day that we are alone with Him.
Whatever we wish for, we ask and He gives us.
Only he who sits with the King receives them. "I have loved you." Malachi 1:2
It is likened to a great wedding feast, and the guests have all left and the bridegroom enjoys us so much he asks us to stay one more day..... so that he can spend quality time with just us.
The Sukkah is not used anymore on this day and the Hallel is recited (psalms 113-118).
Torah references: Lev. 23:36 and Num. 29:35