The Jewish day begins and ends at sundown. All holidays begin the evening of the day preceding the date shown and end the evening of the last day shown. The Jewish year always straddles two years from the civil calendar, since the Jewish calendar begins with Rosh Hashanah. You will notice that spring holidays (such as the Feast of Pesach and Shavuot) occur in the civil year following Rosh Hashanah.

Note: Not all Jewish homes observe two days for holidays shown as lasting two days.

Sukkot is the Feast of Tabernacles or the harvest festival. It commemorates the Israelites' wandering in the desert. Temporary huts called Sukkot are set up to recall those traditionally used during harvest time. It is observed for eight days and culminates with Simchat Torah.
Shmini Atzeret is the Eighth Day of Assembly. Shmini means eight, symbolizing perfection. This holiday is the additional day that brings Sukkot to a state of perfection.
Simchat Torah is the Rejoicing of the Torah. It Celebrates the completion of the reading of the entire Five Books of Moses. A day of assembly, celebration and festivities where Sifrei Torah is paraded around the synagogue.
Shavuot is the Festival of Weeks or the Festival of Harvest. This holiday commemorates Moses and the Jews receiving the Torah from God at Mount Sinai.