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Eid Al-Adha (عيد الأضحى, "the festival of sacrifice") is the biggest Islamic holiday, in which Muslims ritually sacrifice animals (usually sheep) in commemoration of Abraham's attempted child sacrifice of Isma'il (Ishmael). Of the two Islamic Eid festivals (the other being Eid al-Fitr, celebrating the end Ramadan), Eid al-Adha is the holier one. Eid al-Adha occurs on the 10th day of Dhu al-Hijjah, the final month of the Islamic Lunar Calendar, and lasts four days.
In addition to sacrificing an animal, Muslims are instructed to:perform a special congregational Eid prayer in the morning, distribute sweets, and meet with family members. A third of the sacrificed animal is delivered to the poor and the remainder is generally consumed by the family of the individual conducting the sacrifice.
Story of Abraham in the Qur'an
Abraham attempts child sacrifice after receiving instructions to do so from God in his dreams:
My Lord, grant me [a child] from among the righteous."
So We gave him good tidings of a forbearing boy.
And when he reached with him [the age of] exertion, he said, "O my son, indeed I have seen in a dream (في المنام) that I [must] sacrifice you, so see what you think." He said, "O my father, do as you are commanded. You will find me, if Allah wills, of the steadfast."
And when they had both submitted and he put him down upon his forehead
Noteworthy hadith regarding Eid al-Adha
I heard the Prophet (p.b.u.h) delivering a Khutba saying, "The first thing to be done on this day (first day of `Id ul Adha) is to pray; and after returning from the prayer we slaughter our sacrifices (in the name of Allah) and whoever does so, he acted according to our Sunna (traditions)."
Muhammad generally forbade musical instruments and singing girls and said that those who indulge in such would be turned into monkeys and pigs:
It was narrated from Abu Malik Ash’ari that the Messenger of Allah (ﷺ) said: “People among my nation will drink wine, calling it by another name, and musical instruments will be played for them and singing girls (will sing for them). Allah will cause the earth to swallow them up, and will turn them into monkeys and pigs.”
An exception, however, was made for the commemoration of Abraham's attempted child sacrifice:
Abu Bakr came to my house while two small Ansari girls were singing beside me the stories of the Ansar concerning the Day of Buath. And they were not singers. Abu Bakr said protestingly, "Musical instruments of Satan in the house of Allah's Messenger (ﷺ) !" It happened on the `Id day and Allah's Messenger (ﷺ) said, "O Abu Bakr! There is an `Id for every nation and this is our `Id."
"`Id" = "Eid" (the first letter ع has no corresponding letter in English alphabet, so it is transliterated in many ways).
And engage in Jihad
During Eid al-Adha Muhammad used to give sermons (khutbas) and then send Muslims on military expeditions:
Narrated Abu Sa`id Al-Khudri:
The Prophet (ﷺ) used to proceed to the Musalla on the days of Id-ul-Fitr and Id-ul-Adha; the first thing to begin with was the prayer and after that he would stand in front of the people and the people would keep sitting in their rows. Then he would preach to them, advise them and give them orders, (i.e. Khutba). And after that if he wished to send an army for an expedition, he would do so; or if he wanted to give and order, he would do so, and then depart. The people followed this tradition till I went out with Marwan, the Governor of Medina, for the prayer of Id-ul-Adha or Id-ul-Fitr. When we reached the Musalla, there was a pulpit made by Kathir bin As-Salt. Marwan wanted to get up on that pulpit before the prayer. I got hold of his clothes but he pulled them and ascended the pulpit and delivered the Khutba before the prayer. I said to him, "By Allah, you have changed (the Prophet's tradition)." He replied, "O Abu Sa`id! Gone is that which you know." I said, "By Allah! What I know is better than what I do not know." Marwan said, "People do not sit to listen to our Khutba after the prayer, so I delivered the Khutba before the prayer."