Summary: Lady Zainab (as) was (accurately) the third child born to Lady Fatima az-Zahra (sa).{1} She is the daughter of Imam Ali (a) and the Lady Fatima al-Zahra' (a). She was born in Medina in Jumada l-Ula 5, 5 or 6/October 5 626 or 627.{2} 'Abd Allah b. Ja'far was her husband. She and her two sons accompanied Imam al-Husayn (a) in the event of 'Ashura' where her two sons were martyred and she was taken as captive to Kufa and then to Damascus.
Lady Zainab (as) was (accurately) the third child born from Lady Fatima az-Zahra (sa).{1} She is the daughter of Imam Ali (a) and the Lady Fatima al-Zahra' (a). She was born in Medina in Jumada l-Ula 5, 5 or 6/October 5 626 or 627.{2} 'Abd Allah b. Ja'far was her husband. She and her two sons accompanied Imam al-Husayn (a) in the event of 'Ashura' where her two sons were martyred and she was taken as captive to Kufa and then to Damascus.
Her birth anniversary is celebrated every year in the Islamic Republic of Iran as the Day of Nurse, because of her role in nurturing Islam back to life after the tragedy of Karbala. But Zainab (SA) was no ordinary woman. In fact, she was faith personified.
When she was born, her grandfather, the Prophet was out of town, and in respect of him, the proud parents of the baby girl, did not give her any name until he came back. When he returned to Medina, Prophet Mohammad (SAWA), as usual first and foremost went to the house of his immaculate daughter, Hazrat Fatema (peace upon her). He took the baby girl in his arms and said that God has commanded him through the Archangel Gabriel to name her Zainab.{3}
It was no ordinary name. As a matter of fact, it is a compounded term of two Arabic words, that is, Zain and Ab, which means Ornament of the Father. Indeed, Zainab (SA), when she grew up, became such a worthy ornament of Imam Ali (AS) that her sermons in the court of the tyrant Yazid after the tragedy of Karbala, shook Damascus to its very foundations and brought to the audience the memories of the One and Only Commander of the Faithful.
Footnote:
1) Ibn 'Asakir, A'lam al-nisa', p.189-190
2) Mahallati, Rayahin al-shari'a, vol.3 p.33; Muhammadi Ishtihardi, Hadrat i Zaynab, p.17
3) Al-Qurashi, al-Sayyida Zaynab, p.39; Ilahi, Zaynab kubra, p.29; Arfa', Hazrat Zaynab, p.7
Source: http://en.wikishia.net/view/Lady_Zaynab_%28a%29#cite_note-4