A’shuraa’ is the tenth day of Muharram on which Allah, the Almighty, rescued Moses and his followers (the children of Israel) from their enemy. Ibn ‘Abbaas (may Allah be pleased with them both) said, “The Prophet (Allah's peace and blessings be upon him) came to Medina and found the Jews fasting on the day of ‘Ashuraa’. He asked, “What is this?” They said, “This is a good day in which Allah saved the Children of Israel from their enemy and Moses (Allah's peace and blessings be upon him) fasted on this day.” He said, “We are worthier of following Moses than you.” So he fasted that day and told the people to fast.” (Al-Bukhari,1865).
There are various prophetic statements that speak of the virtues of fasting the day of ‘Ashuraa’. For instance, Ibn ʿAbbas (may Allah be pleased with them both) said, “I never saw the Messenger of Allah (Allah's peace and blessings be upon him) so keen to fast any day and give it priority over any other than this day―the day of ʿAshuraaʾ, and this month―the month of Ramadhan." Al-Bukhari, 1867).
Evidently, this hadith shows how the Prophet (Allah’s peace and blessings be upon him) was very keen to benefit from this great day.
According to another Hadith, the Prophet (Allah’s peace and blessings be upon him) explains the reward of fasting on this day as follows:
“For fasting the day of ‘Ashuraa’, I hope that Allah will accept it as expiation for the year that went before [i.e. it is a way to have the sins of the past year forgiven]” (Muslim, 1976).
Moreover, it is recommended to fast a day before or after the day of ‘Ashuraa’ because the Prophet (peace and blessings of Allah be upon him) fasted on the tenth, and intended to fast on the ninth if he was to live the coming year. ‘Abdullah ibn ‘Abbas (may Allah be pleased with them both) said: "When the Messenger of Allah (Allah’s peace and blessings be upon him) fasted on 'Ashura' and commanded the Muslims to fast as well, they said, 'O Messenger of Allah, it is a day that is fasted by the Jews and Christians.' The Messenger of Allah (Allah’s peace and blessings be upon him) said, If I live till the next (year), I would definitely observe fast on the 9th.” According to the narration of Abu Bakr: “He meant the day of ‘Ashuraa' too. However, it happened that the Messenger of Allah (Allah’s peace and blessings be upon him) passed away before the next year came.” (Muslim, 1916). To sum up, fasting on the day of ʿAshuraa' alone is recommended as a desirable act of sunnah. If one can fast the ninth and tenth of Muharram, it will be better.