‘Ashura (10th day of Muharram)
This is the tenth day of Muharram, the month of Allah Almighty.

This is because the Prophet said: “And as for fasting on the day of ‘Ashura, I expect that Allah Almighty shall forgive the sins of the year prior to it.” [ Source: Muslim.]

The reason for fasting on this day is in accordance with what was related from the authority of ‘Abdullah ibn ‘Abbas, who said: “When the Prophet ﷺ arrived at Madinah, he found the Jews fasting on ‘Ashura. Then he inquired why (do they fast on that day)? They answered, ‘This a good day, the day Allah Almighty saved the children of Israel from their enemy, and as such Prophet Musa (peace be upon him) fasted thereafter (on that day).’ Then the Prophet said: ‘I have more right to Musa than you.’ Then he fasted and ordered the Muslims to fast on that day.” [ Source: Bukhari.] In another narration by Imam Muslim, the Prophet said, “If I remain (alive) till the next year, I shall fast the ninth day.” [ Source: Muslim.]
source: islamkingdom