ASHURA IN HISTORY
Ibn 'Abbas® reported: "The Prophet (peace be upon him) came to Madinah and found the Jews fasting on the day of 'Ashurah. He said to them: 'What is this fast?' They said: 'A great day. Allah saved Moses (peace be upon him) and the tribes of Israel from their enemies (Pharoah) on this day and therefore, Moses (peace be upon him) fasted on this day.' The Prophet (peace be upon him) said: 'We have more of a right to Moses (peace be upon him) than you,' so he fasted on that day also and ordered the people to fast on that day." (This is recorded by al-Bukhari and Muslim). According to al-Bukhari and Muslim, Musa al-Ash'ari® reported: "The Jews would honor the day of 'Ashurah as an E’id. The Prophet (peace be upon him) said: 'You [Muslims] are to fast on it.'"
The Prophet (peace and blessings be upon him) said, "Fasting the day of 'Ashura' (is of great merits), I hope that Allah will accept it as an expiation for (the sins committed in) the previous year." (Muslim) But this expiation of minor sins comes only if you avoid major sins. It is a big mistake to rely on fasting a single day to "wipe your slate clean." If you neglect your daily Prayers or the fast of Ramadan, or if you backbite, lie, commit adultery or other major sins, fasting on 'Ashura' alone will not atone for your sins.
The 10th of Muharram will fall on the Tuesday 6th December 2011. We can either fast on Sunday 4th and Monday 5th OR Monday 5th and Tuesday 6th.
In order to not be like the Jews, The Prophet (s) said 'Fast the ninth and the tenth, and do not be like the Jews.' Hence we fast these 2 days for that reason.
It is important to note that fasting on these days is only a Sunnah (not obligatory) and as Muslims trying to observe the sunnah it is best. 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.
And Allah knows best.