In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
In this fatwa:
1- Fasting Ashura used to be obligatory for Muslims, until Allah changed that rule.
2- It is highly recommended to fast on Ashura.
3- If you fast on Ashura, Allah will erase the minor sins of the previous year.
Sheikh Waleed Basyouni further explains the significance of Ashura in this video:
Almighty Allah knows best.