Muharram, is the first month of the Islamic calendar.
It is also the month in which Imam Hussein AS (grandson of the Prophet SAWA) was brutally martyred along with his 72 supporters by an army of about 30'000 sent on the order of Yazid in the land of Karbala (current city of Karbala in Iraq). All this happened because Imam Hussein AS refused to accept Yazid (a tyrant alcoholic who had no shame in disobeying the laws of Islam) as Caliph.
Imam Hussein AS and his supporters and family (including about 85 women and children) entered the land of Karbala on the 2nd of Muharram and were surrounded by the army of the enemy on the 3rd.
On the 7th day, the army of Umar'e Sa'ad (Yazid's commander) cut the water supply of the party of Imam Hussein although until the 9th (Tasu'a) they managed to find very little water but from the 9th, all water was finished.
On the tenth, the Imam and his followers were killed and beheaded. Amongst the martyrs were Imam Hussein’s 6 MONTH old son and the 11 and 13 year old sons of Imam Hassan AS.
After the battle, the army attacked the tents of the women and plundered them, lashed them and set their tents on fire and the women and children were taken as captives. They also renewed their horses' horseshoes and rode over the bodies of the martyrs.
The next day, the party of the women and children along with Imam Sajjad (the 4th Imam who was very ill) were moved towards Kufa and then Sham (current Damascus - the place where Yazid ruled). The heads of the martyrs (which had been severed from their bodies and placed on spears) accompanied the women and children on this journey.
When the party of the captives were moved through the cities, the people were told that they (who were in fact the progeny of the Prophet SAWA and the best of Muslims) were Kafirs and people stoned them and celebrated their sorrow. The Umayyad’s announced this day as Eid and celebrated it for many years.
Shia (and some Sunnis) still mourn the event, especially on the first 10 days of Muharram and more specifically on the 9th (Tasu'a) and 10th (Ashoora).