In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
Dear sister, we would like to thank you for the great confidence you place in us, and we implore Allah Almighty to help us serve His cause and render our work for His Sake. May Allah reward you abundantly for your interest in knowing the teachings of your religion, Islam!
As a matter of fact, the true Muslim always takes the advantage of the blessed occasions and days of Islam. He spares no efforts in drawing himself nearer to Allah. In doing so, he concerns himself with knowing the virtuous days and occasions in Islam so as to follow his Prophet's suit in all spheres of life.
Ibn `Abbas (may Allah be pleased with them both) said: “I never saw Allah’s Messenger (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 `Ashura', and this month, meaning Ramadan.” (Al-Bukhari, Hadith 1867) In another hadith we are told that fasting the day of `Ashura' expiates the sins of the previous year as theProphet (peace and blessings be upon him) said, “Fasting the day of `Ashura' (is of great merits), I hope that Allah will accept it as anexpiation for (the sins committed in) the previous year”(Muslim).
Focusing more on the question in point, Dr. MuzammilH. Siddiqi, former President of the Islamic Society of North America, states,
Fasting the Day of `Ashura' is not to mourn the martyrdom of imamHusain (may Allah be pleased with him). We deeply respect Imam Husain’s martyrdom,we honor his glorious act of sacrifice for the sake of Islam. He gave us a great example of truth, courage and piety. But we also feel pain and grief in our hearts for his assassination at the hand of some hypocrites who took Islam as a pretext to commit their crime. They fought and killed Allah’s Messenger’s beloved and blessed grandson and his family. This was the most heinous and shameful crime that was committed for the sake of political power. This tragic event took place in the year 61 AH or 680 CE. However, the tradition of `Ashura' fasting is very ancient and it goes back to a long time before imam Husian.
It is reported in the Sahih of Imam Al-Bukhari and other authentic collections of hadith that the Prophet (peace and blessings be upon him) and his Companions used to fast on the 10th day of Muharram while they were in Makkah (before the hijrah).
It was a day on which people of Makkah used to change the covering (kiswah) of the Ka`bah. Quraysh also used to fast on this day. (Al-Bukhari, hadith 1489 and 1760)
After the hijrah when the Prophet (peace and blessings be upon him) came to Madinah, he found that the Jews of Madinah also used to observe this day with fasting. The Prophet (peace and blessings be upon him) asked them the reason of their fasting on this day. They said, “This is a blessed day. On this day Allah saved the Children of Israel from their enemy (in Egypt) and so Prophet Musa fasted on this day giving thanks to Allah.” The Prophet (peace and blessings be upon him) said, “We have more claim to Musa than you.” He fasted on that day and commanded Muslims to fast on this day. (Al-Bukhari, hadith 1865)
In another report it is mentioned that Jews of Madinah used to hold a feast on this day. The Prophet (peace and blessings be upon him) told his Companions to fast instead. (Al-Bukhari, hadith 1866)
`Ashura' fasting was obligatory (fard) in the beginning. In the second year of hijrah (624 CE) when Allah’s command came that Muslims should fast the whole month of Ramadan, the Prophet (peace and blessings be upon him) then sent someone to announce to people that fasting of `Ashura' had become voluntary (nafl). This indicates that whosoever wishes to fast, may fast and whosoever does not want to fast, there will be no blame on him/her.
Imam At-Tirmidhi mentioned that ibn `Abbas(may Allah be pleased with them both) used to say that we should fast on two days: the 9th and 10th of Muharram to distinguish ourselves from the Jewish community. (At-Tirmidhi)
Ibn`Abbasalso quoted the Prophet (peace and blessings be upon him) as saying, “If I live next year, I shall also fast on the 9th day.” (MusnadAhmad ibnHanbal, hadith2002)
There is a great reward in fasting the day of `Ashura'. There are many hadiths that mention its blessings and virtues. It is good to fast on this day, although it is not obligatory.
Allah Almighty knows best.
Excerpted, with slight modifications, from: http://pakistanlink.com