In Judaism, today is Shemini Atzeret ("eighth day"), the holy day devoted to the spiritual aspects of the seven-day Sukkot festival which immediately precedes it. It is mentioned in Leviticus 23:39 in conjunction with Sukkot (see also Numbers 29:35; Nehemiah 8:18; 2 Chronicles 7:9). As this site indicates, "Although the observances of Shemini Atzeret generally share the characteristics of the rest of Sukkot, there are four significant differences. The first is that there is no more shaking of the lulav and etrog. Second is that although we have our meals and recite Kiddush in the sukkah (though customs vary), we no longer say the blessing to sanctify us through the commandment to dwell in it, as we did the previous seven days. The third is that in the synagogue, after the Torah reading, we recite the memorial prayer (Yizkor). And finally, the special prayer for rain (Geshem) is added to the repetition of Musaf and thus begins the period of an additional call for rain in our prayers, which lasts until Passover..."
Shemini Atzeret is closely related to tomorrow's day, Simchat Torah. In the Land of Israel, the two festivals are celebrated on the same day.