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.
1- A Muslim is to be keen to get closer to Allah and draw nearer to Him all the time. Such keenness gains more weight and significance during blessed occasions and times.
2- One of these occasions in which a Muslim should exert more effort and show more keenness is the month of Muharram.
3- Muharram is the first month of the Hijri calendar and is one of the four sacred months.
Answering your question, the Fatwa Center at Islam Q and A, states:
Indeed, the sacred month of Muharram is a blessed and important month. It is the first month of the Hijri calendar and is one of the four sacred months concerning which Allah says, “Verily, the number of months with Allah is twelve months (in a year), so it was ordained by Allah on the Day when He created the heavens and the earth; of them, four are sacred. That is the right religion, so wrong not yourselves therein.” (At-Tawbah 9:36)
Abu Bakrah (may Allah be pleased with him) reported that the Prophet (peace and blessings be upon him) said: “Time has come back to its original state which it had when Allah created the Heavens and the Earth; the year is twelve months, four of which are sacred. Three of them are in succession: Dhul-Qidah, Dhul-Hijjah and Al-Muharram, and (the fourth being) Rajab Mudar (named after the tribe of Mudar as they used to respect this month) which stands between Jumad (ath-Thani) and Shaban.” (Al-Bukhari)
Muharram is called so because it is a sacred (muharram) month and to confirm its sanctity. Allah Almighty says, “so wrong not yourselves therein“, which means do not wrong yourselves in these sacred months, because sin in these months is worse than in other months.
It was reported that Ibn Abbas said regarding the above verse that these four months were singled out and made sacred. Sins in these months are more serious and good deeds bring a greater reward.
Qatadah said concerning this phrase “so wrong not yourselves therein” that:
“Wrongdoing during the sacred months is more serious and more sinful than wrongdoing at any other time. Wrongdoing at any time is a serious matter, but Allah gives more weight to whichever of His commands He will.
Allah has chosen certain ones of His Creation. He has chosen from among the angels Messengers and from among mankind Messengers. He chose from among speech His remembrance or dhikr. He chose from among the earth the mosques, from among the months Ramadan and the sacred months, from among the days Friday and from among the nights laylat al-qadr, so venerate that which Allah has told us to venerate.
People of understanding and wisdom venerate the things that Allah has told us to venerate.” (Summarized from the Tafseer of Ibn Kathir, may Allah have mercy on him. Tafseer of Surat at-Tawbah, verse 36).
The Virtue of Observing More Voluntary Fasting during Muharram:
Abu Hurairah (may Allah be pleased with him) said: The Messenger of Allah (peace and blessings be upon him) said: “The best of fasting after Ramadan is fasting Allah’ month of Muharram.” (Muslim)
The phrase “Allah’s month”, connecting the name of the month to the name of Allah in a genitive grammatical structure, signifies the importance of the month.
“The apparent meaning of the above hadith is to fast all of the month of Muharram. But it was proven that the Prophet (peace and blessings be upon him) never fasted any whole month apart from Ramadan, so this hadith is probably meant to encourage increasing one’s fasting during Muharram, without meaning that one should fast for the entire month.
It was reported that the Prophet (peace and blessings be upon him) used to fast more in Sha`ban because he may have not learnt of the virtue of Muharram until the end of his life, before he was able to fast during this month, or because certain circumstances may happened during this month hindering him from fasting such as sickness, travel, etc.” (Sharh al-Nawawi `ala Saheeh Muslim).”
Thus, a true Muslim has to seize the opportunity of these blessed days and tries his best to get as much reward in them as possible.
Allah Almighty knows best.