Why fasting 25 hours on Yom Kippur?

Shalom Isaac! You asked a good question! The day of Yom Kippur itself, the 10th of Tishrei, is 24 hours, but in addition, there’s a mitzvah to add a little from the 9th of Tishrei because the Torah says in one place (Vayikra 23, 32), “from the ninth day of the month in the evening”, instead of just saying the usual “tenth of the month”. In addition, because there is room to count the end of the day (and the beginning of the next day) either from sundown or alternatively from when the stars appear, because Yom Kippur (and Shabbat, as well) is so important, we don’t want to “take a chance” and to be safe, we accept her according to the earlier opinion (sundown), but end her according to the stricter opinion (appearance of 3 medium stars). K’tiva vaChatima Tova to you and your family and all of Israel! Rav Ari Shvat