Ashura falls on the tenth day of the Islamic month of Muharram, and is among the most widely and intensely celebrated of holidays in Muslim lands, including in Bangladesh. Its date will vary, and generally move 11 days earlier each year, on the Gregorian Calendar.
Shia Muslims in particular will observe Ashura in Bangladesh. They will remember the killing of Muhammad's grandson, Hussein Ibn Ali, in the Battle of Karbala in modern day Iraq in A.D. 680 or so. They will even mourn for him throughout the day.
But it is also believed that Moses parted the Red Sea, Noah left the Ark, and that Muhammad fled to Medina on the tenth of Muharram, and these are remembered during Ashura as well.
As Hussain Ibn Ali was brutally killed along with his whole family on this day, it is a time to mourn and to remember the injustices of the world. It was actually directly after the Battle of Karbala that Ibn Ali was killed. And the tragedy has long been committed to poetry, some of which will be recited by Muslims on Ashura.