In her life Zainab (s.a.) always saw the evildoers, oppressors, insurgents and breakers of covenants defy the truth and Imam Ali (a.s.), the supporter of the truth and justice had to quell their revolts. Finally, an evil hand gave Imam Ali (a.s.) a stroke from a poisoned sword on his head in the mosque of Kufa. After Imam Ali (a.s.), his son Imam Hassan (a.s.) became the Caliph. Hassan was also greatly oppressed until at last he signed a peace treaty with the ruler of that time and moved to Kufa in the company of Zainab, her husband, and his own companions. Imam Hassan (a.s.) was poisoned by his treacherous wife Joda, by the order of the Caliph of that time. After Imam Hassan, Imam Hussain (a.s.) became the Imam, but the ruler of Syria Mavia violated the peace treaty and appointed his son Yazid as his successor and insisted that Imam Hussain (a.s.) should pledge allegiance to him. Imam Hussain refused to pledge allegiance and made up his mind to move to Mecca.
Hazrat Zainab (s.a.) said farewell to her husband and went with her brother accompanied by her sons Muhammad and Aun. They reached Mecca in 61 Hijra year.
Imam Hussain (a.s.) was informed that some agents of the ruler of that time had come to Mecca to assassinate him while circumambulating the Holy Ka"bah. Imam Hussain (a.s.) deemed it advisable to move to Kufa and let people know of his secret mission.
They arrived at Karbala on the 2nd Muharram. Zainab had heard from her grandfather and father that Karbala would be the place where Imam Hussain (a.s.) would be martyred.
source : www.tebyan.net