The day on which Imam Hussain (pbuh) was killed by Yazid's army.
Useful information:
QUESTION: We know that the Ashura-day is sad because Yezid's army killed Imam Hussain (as) (the master of the paradise's youths) on this day. But Sunni brothers consider this day as happy day, and they fast it, and they say on Ashura, Allah has saved Moses (as) and they give many ahadeeth regarding this. Please give more details about Ashura day (itself), and the Prophet (s) a hadith regarding this day.
ANSWER: Yes sources do exist about ahadeeth that the 10th of Muharram was regarded in the early days as an auspicious day. Whatever the origin of these ahadeeth, the 10th of Muharram 61 AH turned that day into the day of mourning. Subsequently Banu Umayya as well as the later Sunni regimes did attempt to re-establish the Ashura Day as an auspicious day as a means of diverting attention from the tragedy of Kerbala, but the grief and the tears flowing from the eyes of the lovers of Holy Prophet has firmly established the day as a day of mourning. Our jurists have held that fasting is not permitted on that day. In this context you will no doubt be aware that our 7th Holy Imam was born in the month of Safar but because we continue to mourn Imam Hussain then, we celebrate the birth of the 7th Imam in the month of Rajab.