The day after the last day of Yom Tov is known as Isru Hag and has the status of a minor holiday . There was a custom in Morocco on Isru Hag of Shavuot to gather and bury any Torah scrolls, holy books and holy objects that needed to be buried. When such articles become invalid or unusable, they must be disposed of in a special manner. Since this type of disposal shows honor to the Torah and holy objects, it is fitting to perform the burial after the holiday commemorating our receiving the Torah. Most communities nowadays have a Genizah service in which holy articles can be stored and one should be aware of the intrinsic holiness of even Torah pamphlets, bulletins, etc.
One who has the practice of fasting on the Nahala (Yartzheit) of a family member should not fast if the Nahala falls on Isru Hag, and should postpone it to another day.
Finally, the book Arba Gevi’im discusses a custom to read the books of Iyov, Mishle and Daniel before Minha on the Shabbatot between Shavuot and Tisha B’Av.
Summary: Isru Hag has some properties of Yom Tov. One should be aware of certain articles that may need proper Genizah/disposal if they become unusable.