The day proceeding the day of atonement is unremarkable except that there's an obligation to eat enough that one has an easy fast the next day.
The day of atonement is during the month of Tishrei which has the following "special" days:
Tishrei 1: 1st day of Rosh Hashana "New Year" Holiday.
Tishrei 2: 2nd day of Rosh Hashana. Holiday.
Tishrei 3: Fast day. "Tzom Gedalyia"
Tishrei 9: Eve of Kippour - mitzvah to eat, fast starts at sunset
Tishrei 10: Kippour - day of atonement. Fast ends at nightfall. Holiday.
Tishrei 15: 1st day of Sukkot. Holiday.
Tishrei 16: in Israel: intermediate day of Sukkot - Hol Mamoed - half holiday
Tishrei 16: Outside Israel: 2nd day of Sukkot. Holiday.
Tishrei 17: intermediate day of Sukkot - Hol Mamoed - half holiday
Tishrei 18: intermediate day of Sukkot - Hol Mamoed - half holiday
Tishrei 19: intermediate day of Sukkot - Hol Mamoed - half holiday
Tishrei 20: intermediate day of Sukkot - Hol Mamoed - half holiday
Tishrei 21: intermediate day of Sukkot - "Hoshana Rabba" - half holiday
Tishrei 22: Last day of Sukkot. "Shmini Atzeret". Holiday
Tishrei 23: Outside Israel: last day of Sukkoth. "Simchat Torah". Holiday.