:salam2:
Once our beloved Prophet 
asked Jews that why the fast on the day Ashoora? They replied "because the God saved them from the Pharaoh that is why the fast on this day as a thanks-giving. Prophet said: "In that case we are more close to Prophet Moosa a.s., so He PBUH ordered Muslims to fast on this day.
Before the month of Ramadhan, fasting on this day was obligatory on each Muslim but after the order of fasting in the month of Ramadhan, it become Sunnah and not obligatory.
So Muslim who would like to fast on this day shall not single out a day only but they should fast either a day before or a day after from the day of Ashoora. This is because there are many incident occurred in history.
Please share some history related to this/these days, if any. 