Almighty Allah states in the Holy Quraan:
From out of the four sacred months, Muharram has been blessed with certain specific virtues:-
The Holy Prophet Muhammad (Sallallahu-Alayhi-Wasallam) said:
Although the fasts of the month of Muharram are not obligatory, the one who fasts in these days out of his own will and choice is entitled to a great reward by Almighty Allah.
Although the month of Muharram is a sacred month as a whole, the 10 th of Muharram is the most sacred among all its days. The day is named ‘Ashurah'. It is one of the most important and blessed days of Allah in the Islamic calendar.
According to the Holy companion, Ibn Abbas Radhiallaho Anhu, when the Holy Prophet Sallallahu Alayhi Wassallam migrated to Madinah, he found that the Jews of Madinah used to fast on the 10 th day of Muharram. They said that it was the day on which the Holy Prophet Musa Alayhis Salaam and his followers crossed the Red Sea miraculously, and the Pharaoh was drowned in its water. On hearing this from the Jews, the Holy Prophet Sallallahu Alayhi Wassallam said, “We are more closely related to Musa than you.” So the Prophet Sallallahu Alayhi Wassallam directed the Muslims to fast on the day of Ashura. (Abu Dawood)
According to another Hadith, it is more advisable that the fast of Ashura should be either preceeded or suceded by an additional fast. It means that one should fast two days: the 9 th and 10 th of Muharram or the 10 th and 11 th . The reason of this additional fast as mentioned by the Holy Prophet Sallallahu Alayhi Wassallam is that the Jews used to fast on the day of Ashura alone, and the Holy Prophet Sallallahu Alayhi Wassallam wanted to distinguish the Islmaic-way of fasting from that of the Jews. Therefore, he advised the Muslims to add another fast to the day of Ashura. SOURCE: HERE