The day after the seventh day of Sukkot, Tishri 22, is the holiday Shemini Atzeret.
Shemini Atzeret literally means "the assembly of the eighth (day)." Rabbinic literature explains the holiday this way: our Creator is like a host, who invites us as visitors for a limited time, but when the time comes for us to leave, He has enjoyed himself so much that He asks us to stay another day. Another related explanation: Sukkot is a holiday intended for all of mankind, but when Sukkot is over, the Creator invites the Jewish people to stay for an extra day, for a more intimate celebration.
Shemini Atzeret is a holiday in its own right and does not involve some of the special observances of Sukkot. We do not take up the lulav and etrog on these days, and our dwelling in the sukkah is more limited, and performed without reciting a blessing.
Shemini Atzeret is a day on which work is not permitted.
Source: Bard, Mitchell G. Jewish Holidays: Shemini Atzeret, 1998