Holy Prophet Saw Said in Sahih Muslim: The best month for fasting after Ramadan is fasting in Allah’s month of Muharram. In Arabic the word Ashura means 10th and Fasting on this day is even more Important according to ahadees. In Hadees regarding the Fasting on day of Ashura Holy Prophet Saw said It atones for the sins of the preceding year. Sahih Muslim.
Regarding Fasting on 9th and 10th Muharram or 10th and 11th Muharram instead of only on 10th Muharram: When the Prophet Saw fasted on the day of Ashura commanded that it should be observed as a fast his companions said to him: Messenger of Allah, it is a day which the Jews and Christians hold in high Esteem. Thereupon the Messenger of Allah (Pbuh) said: Next Year Allah willing we would observe fast on the 9th Muharram as well But the Messenger of Allah (peace be upon him) died before the advent of the next year.
10th Muharram in History:
Rasool Allah Saw migrated from Makkah to Madina on this day.
Farone was drowned in water on this day.
Nation of Prophet Moses got freedom on this day.
Hadrat Ali R.a Killed Marhab this day.