The month of Muharram is the first month of the Muslim Calendar, and it is one of the four sacred months of Allaah. Allaah says (interpretation of the meaning): 

“Verily, the number of months with Allaah is twelve months (in a year), so was it ordained by Allaah on the Day when He created the heavens and the earth; of them four are Sacred (i.e. the 1st, the 7th, the 11th and the 12th months of the Islamic calendar). That is the right religion, so wrong not yourselves therein”

[al-Tawbah 9:36] 

al-Bukhaari (3167) and Muslim (1679) narrated from Abu Bakrah (may Allaah be pleased with him) that the Prophet (peace and blessings of Allaah be upon him) said: “The division of time has turned to its original form which was current the day Allaah created the heavens and earth. The year consists of twelve months of which four are sacred: three consecutive months, Dhu’l-Qa’dah, Dhu’l-Hijjah and Muharram, and Rajab of Mudar which comes between Jumada and Sha’baan.” 

It was proven from the Prophet (peace and blessings of Allaah be upon him) that the best fasting after Ramadaan is fasting in the month of Muharram. It was narrated that Abu Hurayrah (may Allaah be pleased with him) said: The Messenger of Allaah (peace and blessings of Allaah be upon him) said: “The best fasting after Ramadaan is the month of Allaah Muharram, and the best prayer after the obligatory prayer is prayer at night.” Narrated by Muslim, 1163. 

With regard to the phrase “the month of Allaah”, mentioning the month in conjunction with Allaah is a sign of its great status. Al-Qaari said: it seems that what is meant is all of the month of Muharram. 

But it was proven that the Prophet (peace and blessings of Allaah be upon him) did not fast any month in full apart from Ramadaan, so this hadeeth is to be understood as meaning that it is it is encouraged to fast a lot in the month of Muharram, not to fast the whole month.