Short answers, pulled from the story.
Husayn ibn Ali was born on the 11th of January 626 in Medina, the son of Ali ibn Abi Talib and Fatima, daughter of the prophet Muhammad. He is revered in Shia Islam as the third Imam. Both Sunni and Shia Muslims regard him as a martyr; his death at the Battle of Karbala on the 10th of October 680 is considered the foundational event of Shia religious identity.
Husayn refused because Yazid's appointment as successor violated the Hasan-Mu'awiya treaty, which stipulated that Mu'awiya would not name a successor. Husayn wrote to Muhammad ibn al-Hanafiyya that his goal was to correct corruptions in the nation, command good, forbid evil, and follow the way of his grandfather Muhammad and father Ali.
On the 10th of October 680, Husayn's force of about seventy-two men was attacked by an Umayyad army commanded by Umar ibn Sa'd at the plain of Karbala, 70 km north of Kufa. After a day of fighting, Husayn was struck by arrows, surrounded, and killed by a soldier named Sinan ibn Anas. Approximately seventy or seventy-two people died on Husayn's side, including members of his immediate family.
Ashura is the tenth day of the Islamic month of Muharram and marks the anniversary of Husayn's death at Karbala. It is observed by Shia Muslims with mourning processions, chest-beating, public gatherings called majalis, and in some communities acts of self-flagellation. The earliest recorded public commemoration took place in Baghdad in 963 during the reign of the first Buyid ruler Mu'izz al-Dawla.
Husayn ibn Ali's tomb is located in the city of Karbala, approximately 90 km southwest of Baghdad. The tomb likely took formal shape about two centuries after the battle and was rebuilt and expanded under successive Abbasid, Dailami, and Ottoman rulers. The city of Karbala grew up around it over time.
Before 680, the pro-Alid movement was primarily a political faction without distinct theology or rituals. The scholar Heinz Halm describes Husayn's death as the "big bang" that created Shi'ism as a religious identity. Karbala gave the community a shared theology of martyrdom, specific mourning rituals, and a collective memory that distinguished it permanently from Sunni Islam.