"On the eighth day you shall have a holy day..." (Vayikra 23:35)
The last day of Sukkos (two days in chutz la'aretz) is also a day
of rest, called Shemini Atzeres. This is actually a separate holiday from
Sukkos and we no longer say the berachah when we eat in the sukkah
on this day. It is also referred to as "zeman simchaseinu," the
time of our joy, and it is when our joy is at its peak.
We also conclude the yearly cycle of the Torah reading on this day, and it
is therefore known as Simchas Torah. Simchas Torah is the ninth day of
the festival in chutz la'aretz, while in Eretz Yisrael it is
celebrated on the eighth day. We dance in circles (hakafos) around
the bimah in celebration of our conclusion of the Torah.