It states (Tehillim 139:16), בהם אחד ולו יצרו ימים, "Hashem created days, and one of the days is Hashem's." Tana d'Bei Eliyahu (ch.1) writes that this refers to Yom Kippur. Yom Kippur is "Hashem's day" because He is so happy that we are being cleansed of our aveiros. The Tana d'Bei Eliyahu writes, "Hakadosh Baruch Hu gave this day to the Jewish nation with love and joy. It can be compared to servants who cleaned the king's palace, and when the king went outside and saw all the garbage that was discarded, he was pleased. This is what happens on Yom Kippur when Hashem forgives the sins of the Jewish nation. Hashem is pleased and says, 'Rejoice immensely because I am forgiving the sins of the Jewish people.'"
The Midrash (Tana d'Bei Eliyahu Zuta, end of ch.4) states, "Moshe went up on Har Sinai for forty days. On the fortieth day [Yom Kippur], the Jewish nation declared a fast day. The fast began at night, and in the morning, they went towards Har Sinai. They were crying as they approached Moshe, and Moshe was crying as he approached them. Their cries went up before Hashem, and Hashem's compassion was aroused, and He accepted their teshuvah. Hakadosh Baruch Hu said, ‘Bnei Yisrael! I swear by My name and throne that your tears will become tears of immense joy. This day will be a day for atonement for you, your children, your grandchildren, and for all generations.'"
