The next upcoming Ashura starts on sundown of August 28th ending at sundown on Saturday, August 29th, 2020.
For Shia Muslims this is a day of sadness and morning where some people will make pilgrimages to a shrine (Mashhad al-Husayn) in Karbala Iraq. Some Sunni Muslims use this day to morn the loss of Husayn and other use the day for fasting because they believe God gave victory to Moses on this day by parting the Red Sea.
The date of Ashura always falls on the 10th day of the 1st month of Muharram according to the Islamic calendar. The date is different each year on the Gregorian calendar system because it is based off of the solar cycle vs the lunar cycle for the Islamic calendar.