Our Prophet Muhammad (pbuh) said, "The best fasting after Ramadan is the month of Allah’s Muharram, and the best prayer after the obligatory prayer is the prayer at night." [Muslim].
Narrated by Ibn Abbas (ra), "I never saw the Messenger of Allah (pbuh) so keen to fast any day and give it priority over any other than this day, the day of Ashura and this month, meaning Ramadan.” [Al-Bukhari]
InshaAllah the reward for fasting the Day of Ashura is to have one's minor sins from the previous year erased ~ The Prophet (pbuh) said, “Fasting the day of Ashura' (is of great merits), I hope that Allah will accept it as an expiation for (the sins committed in) the previous year” [Muslim].
The Prophet (pbuh) highly encouraged us to fast the 9th of Muharram along with the 10th, and if you are unable to fast the 9th & 10th, then try to fast the 10th & 11th.
It is also very beneficial to fast the three white days (13th, 14th & 15th) of each lunar month.
May Allah (swt) help us to make the most of these golden opportunities and accept our deeds, ameen!