He is the second son of Abraham from his wife Sarah and his birth occurred after Ibrahim (Abraham) and his wife left their pagan people who worshipped Idols.
The Annunciation of Isaac's birth to Abraham
As is the case in both Judaism and Christianity, Islam believes that Ishaq (the Arabic form of Isaac) was born after Ishmael ; a miraculous birth, as his mother, Sarah, was old and barren. Angels who came in human shape visited Ibrahim. As Ibrahim was a righteous and hospitable prophet of God, he offered the Angels some food to eat. To his shock, however, the Angels refused to eat. The Angels, however, immediately comforted Ibrahim and told him that they were Angels, sent by God to tell him about the powerful, prophetic son Sarah will soon bear, whom will be called Ishaq. They also told Ibrahim that they were on their way to prophet Lot's people. Ibrahim immediately feared for the safety of Lot but the Angels told him that he shall be informed to run away before his people will receive their punishment from God.
The Sacrifice of Abraham's son
The Qur'an states that Abraham was commanded to sacrifice his son. The son is not however named in the Qur'an. In early Islam, there was a dispute over the identity of the son. However, some Muslim scholars came to endorse that it was Ishmael but some others, notably Muhammad ibn Jarir al-Tabari, who was the most famous and most praised as well as one of the first commentators of the Qur'an stated that it was clearly Isaac and not Ishmael. The argument of those early scholars who believed it was Isaac rather than Ishmael was that "God's perfecting his mercy on Abraham and Isaac" (12:16). Referring to God making Abraham His prophet and saving him from the burning bush, and to his rescuing Isaac. The birth of Isaac happened after Abraham left his people and asked for a child (37:99–113). Many scholars, however, refuse to dispute over the identity of the son as they believe the message in the tale is far more important than the names of the figures involved.
Isaac's legacy in Islam
A revered Prophet and Patriarch, Isaac is seen as one of the many prophets sent by God to guide the Israelites and teach them the message of Islam. His high rank in the righteous line of messengers cannot be overstated, as he was the father of Abraham's Hebrew line, while his brother Ishmael, who is also venerated as a Patriarch and a Prophet, was the father of the Arabs.
There is frequent mention of Isaac in the Qur'an, much of it in lines where he is praised alongside fellow Prophets. Prophet Joseph refers to his grandfather Isaac when describing his beliefs:
And I follow the ways of my fathers,- Abraham, Isaac, and Jacob; and never could we attribute any partners to God: that (comes) of the grace of God to us and to mankind: yet most men are not grateful. (12:38)
In other lines, Isaac is praised alongside fellow messengers of God, as in this verse:
We have sent thee inspiration, as We sent it to Noah and the Messengers after him: we sent inspiration to Abraham, Ishmael, Isaac, Jacob and the Tribes, to Jesus, Job, Jonah, Aaron, and Solomon, and to David We gave the Psalms. (4:163)
In some lines, as in the following verse, the Qur'an mentions the attributes of Isaac:
And commemorate Our Servants Abraham, Isaac, and Jacob, possessors of Power and Vision. (38:46)
Isaac is in total mentioned 17 times in the Qur'an, making him, along with Solomon, the 9th most-mentioned Prophet in the Qur'an.