Muslim reported from Abu Hurayra (Allah be pleased with him), that the Prophet (Allah bless him and give him peace) said, "The best of fasts after the month of Ramadan are in the Month of Allah, which you call Muharram. And the best of prayer after the obligatory prayer is the night prayer." [Muslim, 1163]
This refers to general voluntary fasts according to Imam Ibn Rajab (Allah have mercy on him): These are best in the month of Muharram, just as the best general voluntary prayer is night prayer. The virtue and honour of this month can be attested to by the fact that the Prophet (Allah bless him and give him peace) called it, "the Month of Allah" (Shahr Allah).
It is mentioned in Bukhari and Muslim from Ibn Abbas (Allah be pleased with him and his father) that he was asked about fasting the Day of Ashura [10th of Muharram]. He said, "I did not see the Messenger of Allah (blessings and peace be upon him) fast a day while more avid to seek its virtue than this day," [meaning the Day of Ashura]. [Bukhari (2006), and Muslim (1132)].
The Prophet (Allah bless him & give him peace) used to fast this day even in Mecca, though he had not yet ordered others to do so. [Bukhari (2002), Muslim (1125)] When he migrated to Medina, and found the People of the Book fasting this day and venerating it, he ordered the Muslims to fast it, and encouraged it so much that even the children would fast it. [Bukhari (2004) and Muslim (1130)]
At the end of his life, the Messenger of Allah (blessings and peace be upon him) made the determination not to fast this day alone, but with another day [either before or after it], in order to be different from the People of the Book. It is reported in the Musnad of Imam Ahmad (Allah have mercy on him), from Ibn Abbas (Allah be pleased with him) that the Prophet (Allah bless him and give him peace) said, "Fast the Day of Ashura and be different from the Jews by fasting a day before it or a day after it."
It is a day in which Allah forgave an entire people. Tirmidhi relates that the Prophet (Allah bless him and give him peace) said to a man, "If you want to fast a month after Ramadan, then fast Muharram, for it has a day in which Allah forgave an entire people, and He turns to others who repent." [Tirmidhi (841)]
"Lataif al-Maarif" - Ibn Rajab