The entire month of Muharram is sacred and special and fasting on any day of Muharram has special rewards from Allah, but the 10th day of Muharram, called Ashura holds a more significant position than the rest of the days.
Rasul Allah 
used to fast on the day of Ashura even after fasting in Ramadan was made obligatory.Ibn 'Abbas
reported
When the Messenger of Allah (may peace be upon him) fasted on the day of 'Ashura and commanded that it should he observed as a fast, they (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 (may peace be upon him) said: When the next year comes, God willing, we would observe fast on the 9th But the Messenger of Allah (may peace be upon him) died before the advent of the next year.
[ Musim : Book 006, Hadith Number 2528]
Abdullah ibn Abbas also reported
Abdullah b 'Abbas reported that the Messenger of Allah (may peace be upon him) had said: If I live till the next (year), I would definitely observe fast on the 9th, and the narration transmitted by Abu Bakr is: "He meant the day of Ashura." [ Muslim: Book 006, Hadith Number 252]