Shemini Atzeret -"the Eighth [day] of Assembly"- is celebrated beginning Wednesday night, October 8th. Outside of Israel, a second day is celebrated which is referred to as Simchat Torah ("the Rejoicing of the Torah"). In Israel, the holidays of Shemini Atzeret and Simchat Torah are combined into one and either name can be used to refer to the holiday.
Shemini Atzeret immediately follows the holiday of Sukkot. The special celebrations for this holiday are the
beginning of the prayers for rain, and the celebration of the completion of the yearly reading of the Torah Scroll,
and returning it back to its beginning to start again during Simchat Torah.
Some commentaries focus on the meaning of the name "Atzeret," meaning "to gather" or "store up." He suggests that the sentiments that we have expressed throughout the entire fall holiday season - repentance, reconciliation, renewal - should be gathered up and stored within us for the following year. We hope that as we turn back to the beginning once again, we will store up all the hopes, all the strength that we have, and turn it into our work for the coming year. This year, may we have gathered enough strength to work for peace - and achieve it.