This High Holy Day is in Leviticus 23:39. The New King James Version says:
'Also on the fifteenth day of the seventh month, when you have gathered in the fruit of the land, you shall keep the feast of the LORD for seven days; on the first day there shall be a sabbeth-rest, and on the eighth day a sabbath-rest.'Shemini Atzeret is the day after the Feast of Tabernacles (which is celebrated for seven days) and is the "eighth day" referred to in the verse above. It is a High Holy day to God. It pictures yet another part of God's plan for mankind. The term "Shemini Atzeret" means the assembly of the eighth (day). Other references to the Feasts of God are: Exodus 23:14-16; Exodus 34:22; Leviticus 23:33-36 and 39-43; Numbers 29:12-38; Deuteronomy 16:13-15.
Shemini Atzeret is a separate day from the celebration of the Feast of Tabernacles. It pictures so much more than we as Christians can possibly imagine. Before I come to that, though, it is important to see how the keepers of the oracles of God (Romans 3:1-2), the Jewish people, think about and celebrate this day. Here is a short article on how this day is kept today along with a bit of history: http://judaism.about.com/od/simchattorah/a/all_8atzeret.htm
In the meantime, as we look in the Book of Revelation, we can find something very surprising about this day. Now before you read the rest, please keep in mind that we all see through a glass darkly as the Apostle Paul wrote so what I will say next is possible in sequence with the other High Holy Days and what they picture, but only God knows what will truly happen in the future. Nothing is written in stone as far as what we as humans know. Only God knows what all this means perfectly.
Shemini Atzeret takes place the next day after the seven-day Feast of Tabernacles or Sukkot. The seven-day Feast of Tabernacles pictures the time written in the book of Revelation, chapter 20, verses 4-6. This is when Jesus lives and reigns with those who are in the FIRST RESURRECTION! What? Do you mean there is more than one resurrection? Read it for yourself in Revelation 20:5. Isn't that scripture a bit of a head scratcher for most Christians.
Now if the Bible talks about a first resurrection, the next question is: Does it talk about other resurrections? The answer is that it most certainly does. Go to Revelation 20: 11-15. Here is a section of scriptures that many Bibles title as "The Great White Throne Judgment." But how can that be when most Christians believe that when a person dies, they instantly go to heaven or hell and are judged at death. This is a question that has probably been asked from the time that Revelation was originally written until this day at least among Christians. I would ask you to read what is written and ask God what this means.
In the meantime, notice that this is the judgment for the dead, small and great. They are standing before God. Could this judgment be for those who never knew God. Remember that the dead in Christ were already in the first resurrection when Christ returned a thousand years earlier and were considered the bride at the marriage supper (Revelation 19:7-9). They have lived and reigned with Christ the whole thousand years (Revelation 20:4-6). Now this Great White Throne appears. Could the "Him" that sat on the throne be God the Father. What if there is a time for those in this second resurrection to get to know God and have their names written in the Book of Life between the time they are resurrected and the time they are judged? So many questions. The one thing that we do know is that there are two resurrections. Could it be that God does not give us all the answers and that we see through a glass darkly? I do know that the Bible says that it is God's will that no man should perish and yet I know that God is very fair. Before you jump to any conclusions based on what you have been taught ask God to show you what all of this is. Could it be that God does not clearly define all of this because it is not time to understand all of the details? Could it be that this very High Holy Day and the observance of it is the key to understanding more on this subject? May God bless you as you go to Him with your every need.
In the meantime, be blessed on this High Holy Day that God set forth in the Old Testament. Know beyond a doubt that it looks forward into the plan of God for all mankind and that God is fair, just, and has a plan that goes beyond anything that we can comprehend. Center on the mighty love that God is and live in His light.