In Vayikra 23:36, the Torah tells us "...on the eight day, you
will have a holy day...it is a day of detention ["Atzeres"]...."
The Sefer HaChinuch writes that the Sages have told us that in
reality, Shmini Atzeres is not the eighth day of Sukkos, but
rather a separate holiday, which occurs at the end of the Sukkos
holiday. What was the reason why Hashem commanded us to observe
this day as a holiday? The Sefer HaChinuch explains that Sukkos
is the last holiday of the Jewish calendar [if we consider the
month of Nissan as the beginning of the year, and Pesach the
first holiday]. By giving us this holiday of Shmini Atzeres, its
as if Hashem was telling us "Please, stay with me one more day,
as it is difficult for me to part with you." Hashem, out of his
great love for the nation of Israel, finds it hard to "leave"
his children at the end of the holidays. Therefore, He added on
one more day, so we, the nation of Israel, can spend one more
day with Hashem before our "departure." Now that we understand
the spirit