Shemini Atzeret means “Eighth Day of Assembly.”
It is mentioned in the Torah in Leviticus 23:39, “and on the eighth day [of Sukkot] there shall be a solemn rest.” This is a little complicated, because Sukkot has seven days. So what is the eighth day?
Think of Sukkot as a great party (because it is a great party, after all.) Ancient Jews called it “HaChag,” THE Holiday, because it was the most joyful holiday of the entire year. Now, think about the last great party you attended. Did you leave early, or find yourself staying long after the official ending?
Shemini Atzeret is one more day of rejoicing before the rains start and fall comes and things get cold and dark. In the Diaspora, for reasons I’ve discussed before, it goes on for two days, the second of which is Simchat Torah.
This year (5774, or 2013, if you insist) Shemini Atzeret starts on the evening of Wednesday, Sept 25, continuing until sundown on Sept 26.
I hope you’ve had a great Sukkot!