Ashura falls on the tenth of Muharram, and it is the clearest case in the Islamic calendar of a single date meaning opposite things to different communities.
For Sunni Muslims it is a day of voluntary fasting. The hadith literature reports that the Prophet found the Jews of Medina fasting on that day in commemoration of the deliverance from Egypt, said that Muslims had a greater claim to Moses, and fasted it, adding a recommendation to fast the ninth as well, so as to differ from the Jewish practice. The fast is recommended, not obligatory, and the day's tone is one of gratitude. The connection to the Jewish Day of Atonement, also on the tenth of a month, has been noted since the early period.
For Shia Muslims it is the anniversary of the killing of Husayn, grandson of the Prophet, with his family and companions at Karbala in 680, by forces of the Umayyad caliph Yazid. It is a day of mourning, and the mourning is public and intense: recitation of the narrative in assemblies, processions, elegies, chest-beating, passion plays performed in Iran, and among some communities practices of self-flagellation that a number of senior Shia clerics have discouraged or forbidden.
That the same date carries a fast of thanksgiving in one tradition and the deepest mourning in the other is not a coincidence to be smoothed over. Both observances are old, they have separate origins, and the collision on one day is a durable source of sectarian tension where the two communities live together.