Why is it recommended to fast the 9th and 10th of Muharram?
The fasting the 9th and the 10th of Muharram is a Prophetic Sunnah. The tenth day of Muharram is called “Ashura”. This day commemorates the day when Allah saved the Children of Israel from Pharaoh.
The Prophet (peace and blessings be upon him, PBUH) said, “Fasting the day of Ashura, I hope that Allah will accept it as expiation for the previous year.” (Muslim)
Abdullah ibn Abbas said: When the Messenger of Allah (PBUH) fasted on the day of Ashura and told the people to fast, they said, “O Messenger of Allah, this is a day that is venerated by the Jews and Christians.” The Messenger of Allah (PBUH) said, “Next year, if Allah wills, we will fast on the ninth day.” But by the time the following year came, the Messenger of Allah (PBUH) had passed away. (Muslim)
Based on this, there are different ways of fasting Ashura, the least of which is to fast the 10th. However, it is recommended to fast both the 9th and the 10th because the Prophet (PBUH) was intending to fast both days. The more one fasts in Muharram, the better.
Source: www.islamqa.info