Who was Bibi Zainab bint Ali
Zainab was the third child of Imam Ali and Bibi Fatimah Zahra. She was born in Medina and was named by Prophet Muhammad after her eldest aunt, then deceased.
Zainab lost her mother when she was only three years old and she grew extremely close to her full brothers, Hasan ibn Ali and Hussain ibn Ali.

After the Martyrdoms on Ashura
After the massacre of Imam Hussain bin 'Ali and his companions at Karbala, the forces of Yazid bin Mu'awiyah took the children and women of Hussain's caravan as prisoners. They were taken from Karbala to Kufa and from Kufa to Damascus, the capital and stronghold of Umayyid power.

In the Court of Yazid
In Damascus, the women and children were presented into the court (darbar) of Yazid. Yazid had assembled all the dignitaries and officers of his capital for that occasion. When the prisoners where brought in, they saw that Imam Hussain's head was at the foot of Yazid's thorn.
Yazid was joyfully reciting some poems in which he openly rejected the Prophethood of Prophet Muhammad (s.a.w.) and called on his ancestors (who were killed by the Muslim army in the battle of Badr) to witness the revenge which he had extracted from the family of the Prophet.

It was under such an emotionally charged circumstances that Zainab bin Ali, the courageous daughter of a courageous father, stood up and gave a very moving speech in response to Yazid's statements.

In the name of Allah the, the Beneficent, the Merciful. All praise is due to Allah, the Lord of the Universe, Allah's blessings be on His Messenger's Family altogether.

Allah says: "Then the end of those who do evil deeds is that they reject the verses of Allah and ridicule them". (Quran 30:10)

Oh Yazid! Do you think that by making us prisoners in such a way that we are being taken from one place to another in humiliation - do you think that by this you have humiliated us in the sight of Allah and have earned respect for yourself?!

This apparent success of yours is the result of grandeur of your might and lofty status for which you are proud…. You feel that you have conquered the whole world and your affairs are organised and that our domain is now under you control…
And are you forgetting that Allah has said:

"Surely those who have bought unbelief at the price of faith shall do no harm at all to Allah, and they shall have a painful chastisement". (Quran 3:177)

Then Zainab reminds Yazid that his grandmother and other relatives came into the fold of Islam only after the fall of Mecca at the hands of the Muslims. Since Mecca was taken without any war or bloodshed, legally the entire inhabitant could have been made the slaves of the Prophet.
But the Prophet, out of his mercy, declared to the people of Mecca that
'I release you from the bonds of slavery, you are free.' In other words, Zainab wanted Yazid to remember that his ancestors were the 'freed slaves' of her grandfather.
Look at the courage of Zainab! Standing as a prisoner in the court of Yazid, she does not hesitate to remind him of his reality.

Is it justice, O son of the freed slaves!, that you provide your ladies and slave-girls with hijab, whereas the daughters of the Messenger of God are held prisoners?
You have insulted them by taking away the covers; you have exposed their faces to the enemies -- from one city to another. Everyone irrespective of his high or low status stares at their faces. These ladies do not have their gents or protectors with them.

Then Zainab reminds the audience of the origins of Yazid: his grandmother, Hind (the wife of Abu Sufyan), had ordered her slave after the battle of Uhud to cut open the chest of Hamzah, the Prophet's uncle, and chewed upon his liver to 'quench' her anger for death of her father and brother who were killed in Badr.

But, of course, how can we expect protection from him whose mouth spits out the heart of the pious people, whose flesh has grown from the blood of martyrs? And why should he not hate us who is jealous of us and shamefully say:
'I wish my ancestors had seen me today; they would congratulate me and pray that my hand would never be weak'.
He is saying this while, he is hurting [with his cane] the teeth of Hussain, the leader of the Youths of Paradise.

Why should he not say these things -- he who has cursed his feelings and sores by spilling the blood of Muhammad's family, the stars of the family of 'Abdul Muttalib.

You call your ancestors hoping that they will answer you. You will be put together with them and then you will regret and say had my tongue become dumb so that I would not have said what I said.

O Allah! Give us our right, and avenge those who have oppressed us; and send your anger upon those that spilled our blood and killed our protectors

By Allah! O Yazid, by killing 'Hussain you have not torn but your own skin and you have not cut but your own flesh. You will be brought to the Prophet with the crimes of spilling the blood of his children and humiliating his family.