Virtue of Voluntary Fasting in al-Muharram
Question

Is it Sunnah to observe a lot of nafl [supererogatory] fasts in the month of al-Muharram? Is there anything special about this month compared with other months?
Praise be to Allah.Virtues of al-Muharram
The month of al-Muharram is the first month of the Arabic year, and it is one of the four sacred months of Allah. Allah says (interpretation of the meaning): 
“Verily, the number of months with Allah is twelve months (in a year), so was it ordained by Allah 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-Bukhari (3167) and Muslim (1679) narrated from Abu Bakrah (may Allah be pleased with him) that the Prophet (peace and blessings of Allah be upon him) said: “The division of time has turned to its original form which was current the day Allah 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 al-Muharram, and Rajab of Mudar which comes between Jumada and Sha’ban.” 
Fasting in al-Muharram
It was proven from the Prophet (peace and blessings of Allah be upon him) that the best fasting after Ramadan is fasting in the month of al-Muharram . Abu Hurayrah (may Allah be pleased with him) said: The Messenger of Allah (peace and blessings of Allah be upon him) said: “The best fasting after Ramadan is the month of Allah al-Muharram, and the best prayer after the obligatory prayer is prayer at night.” (Muslim, 1163) 
With regard to the phrase “the month of Allah”, mentioning the month in conjunction with Allah is a sign of its great status. Al-Qari said: it seems that what is meant is all of the month of al-Muharram. 
But it was proven that the Prophet (peace and blessings of Allah be upon him) did not fast any month in full apart from Ramadan, so this hadith is to be understood as meaning that it is encouraged to fast a lot in the month of al-Muharram, not to fast the whole month. 
And Allah knows best.