Muharram is the month with which the Muslims begin their lunar Hijrah Calendar. It is one of the four sanctified months about which the Holy Quran says, "The number of the months according to Allah is twelve months (mentioned) in the Book of Allah on the day in which He created heavens and the earth. Among these (twelve months) there are four sanctified".
These four months, according to the authentic traditions are the months of Zulqadah, Zulhijjah, Muharram and Rajab. All the commentators of the Holy Quran are unanimous on this point, because the Holy Prophet in his sermon on the occasion of his last Hajj, has declared:
"One year consists of twelve months, of which four are sanctified months, three of them are in sequence; Zulqadah, Zulhijjah, Muharram, and the fourth is Rajab."

It is the first month of the Islamic Calendar.
The meaning of the word:- The word "Muharram" means "Forbidden." Even before Islam, this month was always known as a scared month in which all unlawful acts were forbidden, prominently the shedding of blood.
A blessing of Muharram:- There are many bounties of this month, especially the tenth of Muharram.
Two of the many virtues of the 10th of Muharram:
-In this day he who spends more lavishly for the sake of his family members, Allah Taala will bestow blessing upon the sustenance of the following year.
Abu Qataada has related that the Prophet has reported to have said, It is my thought that by fasting on the 10th of Muharram Allah Taala will pardon the sins of the past year. (Tirmizi)

Muharram is one of the sacred months of the year. Fasting this month is highly recommended.
Abu Hurayrah narrated that the Prophet (Sallallaahu alayhi wa sallam) said:
“The best fasting after the month of Ramadaan is the month of Allaah, the Muharram” [Saheeh Muslim]
Allaah's Messenger called this month the month of Allaah and as we know that when this type of idaafah is
mentioned and it is related to the name of Allaah, then it means that object has greatness, honor and deserves our
respect and veneration as is prescribed in the shariah. Like baytullah, naaqatullaah, rosuulullaah….
So, we understand the great importance of this month, however fasting in this month shouldn't be done as a whole
as we know from the sunnah that the Prophet (saw) never fasted a full whole month except the month of
Ramadaan. So, what the hadith in saheeh Muslims means is to fast a lot of days in Muharram – but not the whole
month and Allaah knows best.

1 Muharram is on the 14 October, Wednesday in 2015. Also, Ashura which is the tenth day of Muharram is on the 23 October, Friday. The month of Muharram ends on the 12 December, Thursday.

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 Day of `Ashura has great virtue, and tremendous sanctity (hurma). The virtue of fasting it was known among the Prophets (peace be upon them all). Both Prophet Nuh and Prophet Musa (peace be upon them both) fasted it.

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, as mentioned in both Bukhari and Muslim. [Bukhari (2002), Muslim (1125)]

In April 680, Yazid I succeeded his father Muawiyah as the new caliph. Yazid immediately instructed the governor of Medina to compel Hussayn and few other prominent figures to pledge their allegiance (Bay'ah). Husayn, however, refrained from it believing that Yazid was openly going against the teachings of Islam in public and changing the sunnah of Muhammad. He, therefore, accompanied by his household, his sons, brothers, and the sons of Hasan left Medina to seek asylum in Mecca.

The leader of the small band of men who were martyred in Kerbala was none other than Husain (A), son of Ali bin Abi Talib (A) and grandson of the Holy Prophet (SAV). Who was Husain? He was the son of Fatima (A) for whom the Holy Prophet (SAV) said, "Husain is from me and I am from Husain. May God love whoever loves Husain."

With the passing away of his brother Hasan(A) in 50 AH, Husain (A) became the leader of the household of the Holy Prophet (SAV). He respected the agreement of peace signed by Hasan (A) and Muawiya, and, despite the urging of his followers, he did not undertake any activity that threatened the political status quo. Rather he continued with the responsibility of looking after the religious needs of the people and was recognised for his knowledge, piety and generosity. An example of the depth of his perception can be seen in his beautiful du'a on the day of Arafat, wherein he begins by explaining the qualities of Allah, saying:

Why is Husain (A) regarded as the "leader of the martyrs" ? It is because he was not just the victim of an ambitious ruler. There is no doubt that the tragedy of Kerbala, when ascribed to the killers, is a criminal and terrible act. However when ascribed to Husain (A) himself, it represents a conscious confrontation and a courageous resistance for a sacred cause. The whole nation had failed to stand up to Yazid. They had succumbed to his will, and deviation and regression towards the pre-Islamic ways were increasing.

Passiveness by Husain (A) in this situation would have meant the end of Islam as we know it. Thus Husain (A) took upon himself the responsibility of the whole nation. The greatest tragedy was that one who stood up for the noblest of causes, the defence of Islam, was cut down in so cruel a manner.

Not related to Ashura and Karbala, some Sunni Muslims fast on this day of Ashura based on narrations attributed to Muhammad. Some other Sunnis accept Ashura as a significant day due to the martyrdom of Imam Husayn and the significance of the events at Karbala. The fasting is to commemorate the day when Moses and his followers were saved from Pharaoh by Allah by creating a path in the Red Sea. According to Muslim tradition, the Jews used to fast on the tenth day. So Muhammad recommended to be different from the Jews and recommended fasting two days instead of one. This quote has been said many times but there is no valid hadees from any authentic source. 9th and 10th or the 10th and 11th day of Muharram.

For Shi'a Muslims, rituals and observances on Ashura consist primarily of public expressions of mourning and grief. Some Shi'as express mourning by flagellating themselves on the back with chains, beating their head or ritually cutting themselves. This is intended to connect them with Husayn's suffering and death as an aid to salvation on the Day of Judgment.

Passion plays commemorating the death of Husayn are also presented on Ashura. In London, around 3,000 Shi'a Muslims gather at the Marble Arch on Ashura for a mourning procession and speeches.

Many Shi'a make pilgrimages on Ashura to the Mashhad al-Husayn, the shrine in Karbala, Iraq, that is traditionally held to be Husayn's tomb.

Husayn's martyrdom is widely interpreted by Shia as a symbol of the struggle against injustice, tyranny, and oppression.

The 12 months of the calendar are:

Muharram
Safar
Rabi' al-awwal (Rabi' I)
Rabi' al-thani (Rabi' II)
Jumada al-awwal (Jumada I)
Jumada al-thani (Jumada II)
Rajab
Sha'ban
Ramadan
Shawwal
Dhu al-Qi'dah
Dhu al-Hijjah

Islamic New Year - 1 Muharram: 14 October 2015
Day of Ashura - 10 Muharram: 23 October 2015
Mawlid an-Nabi - 12 Rabi al-Awwal: 23 December 2015
Laylat al Miraj - 27 Rajab: 4 May 2016
Laylat al-Baraat: 15 Shaban: 22 May 2016
First day of Ramadan : 1 Ramadan: 6 June 2016
Laylat al-Qadr - 19,21,23,25,27 or 29 Ramadan: Between 25 June - 4 July 2016
Eid al-Fitr - 1 Shawwal: 6 July 2016
Eid al-Adha- 10 Dhu al-Hijja: 11 September 2016

The Islamic religious year is known as Hijri year. It began with the Hijrah of the Prophet Muhammad (PBUH) from Makkah to Madinah in the year 622 of the common era. The twelve-month year is based on a purely lunar cycle of 354 days. Thus Islamic dates have no fixed relation to the seasons of the 365 day solar year. Over the course of years all Islamic events may occur in spring, summer, autumn or winter.
Twelve Islamic months are as follows:

Muharram ul Haram
Safar
Rabi-ul-Awwal
Rab-ul-Akhir
Jamadi-ul-Awwal
Jamadi-ul-Akhir
Rajab
Sha’aban
Ramadhan
Shawwal
Dhul Qadah
Dhul Hijjah

Yes, people can fast on Mawlid to welcome the night of the Prophet's birthday and with the intention of worship if they want.
There is nothing in the Qur’aan to say that we should celebrate the Mawlid or birthday of the Prophet (peace and blessings of Allaah be upon him). The Prophet himself (peace and blessings of Allaah be upon him) did not do this or command anyone to do it, either during his lifetime or after his death. Indeed, he told them not to exaggerate about him as the Christians had exaggerated about Jesus (upon whom be peace). He said: “Do not exaggerate about me as the Christians exaggerated about the son of Maryam. I am only a slave, so say, ‘The slave of Allaah and His Messenger.’” (Reported by al-Bukhaari).

“The key to the prayer (salah) is cleanliness, its beginning is takbir (saying Allahu Akbar) and its ending is salam (salutation).” (Abu Dawud, Taharah, 31: Tirmidhi, Taharah, 39)
“Keep cleaning so that your sustenance will increase...”.

“Islam is clean. Therefore, you should keep yourselves clean, too. Only the clean people can enter Paradise.” (Hadith)

“Cleanliness is the half of belief.” (Hadith)

“Cleanliness is from belief (its perfection and light).” (Hadith)

“Islam was built on the foundation of cleanliness.”

“Allah is clean; He loves clean people.”