The word udhiyah means an animal of the ‘an’aam class (i.e., camel, cow, sheep or goat) that is slaughtered during the days of Eid al-Adha because of the Eid and as an act of worship, intending to draw closer to Allah thereby.
This is one of the rituals of Islam prescribed in the Book of Allah and the Sunnah of His Messenger (peace and blessings of Allah be upon him), and according to the consensus of the Muslims.
In the Qur’aan:
1 – Allah says (interpretation of the meaning):
“Therefore turn in prayer to your Lord and sacrifice (to Him only)” [al-Kawthar 108:2]
2 – Allah says (interpretation of the meaning):
“Say (O Muhammad): Verily, my Salaah (prayer), my sacrifice, my living, and my dying are for Allah, the Lord of the ‘Aalameen (mankind, jinn and all that exists).
He has no partner. And of this I have been commanded, and I am the first of the Muslims” [al-An’aam 6:162]
The word nusuk (translated here as sacrifice) means sacrifice; this is the view of Sa’eed ibn Jubayr. And it was said that it means all acts of worship, including sacrifice, which is more comprehensive.
3 – Allah says (interpretation of the meaning):
“And for every nation We have appointed religious ceremonies, that they may mention the Name of Allah over the beast of cattle that He has given them for food. And your Ilaah (God) is One Ilaah (God Allah), so you must submit to Him Alone (in Islam). And (O Muhammad) give glad tidings to the Mukhbitoon [those who obey Allah with humility and are humble from among the true believers of Islamic Monotheism]” [al-Hajj 22:34]
In the Sunnah:
1 – It was narrated in Saheeh al-Bukhaari (5558) and Saheeh Muslim (1966) that Anas ibn Maalik (may Allah be pleased with him) said: “The Prophet (peace and blessings of Allah be upon him) sacrificed two white rams speckled with black. He slaughtered them with his own hand, said ‘Allahu akbar’ and put his foot on their necks.”
2 – It was narrated that ‘Abd-Allah ibn ‘Umar (may Allah be pleased with him) said: “The Prophet (peace and blessings of Allah be upon him) stayed in Madeenah for ten years, offering sacrifice (every year on Eid).” Narrated by Ahmad, 4935; al-Tirmidhi, 1507; classed as hasan by al-Albaani in Mishkaat al-Masaabeeh, 1475.
3 – It was narrated from ‘Uqbah ibn ‘Aamir (may Allah be pleased with him) that the Prophet (peace and blessings of Allah be upon him) shared out sacrificial animals amongst his companions, and ‘Uqbah got a sheep that was six months old. He said, “O Messenger of Allah, I got a sheep that is six months old.” He said, “Offer it as a sacrifice.” Narrated by al-Bukhaari, 5547.
4 – It was narrated from al-Baraa’ ibn ‘Aazib (may Allah be pleased with him) that the Prophet (peace and blessings of Allah be upon him) said: “Whoever offers a sacrifice after the prayer has completed his rituals (of Eid) and has followed the way of the Muslims.” Narrated by al-Bukhaari, 5545.
The Prophet (peace and blessings of Allah be upon him) offered sacrifices, as did his companions (may Allah be pleased with them). And he said that sacrifice is the way of the Muslims.
The Sunnah indicates that the one who wants to offer a sacrifice must stop cutting his hair and nails and removing anything from his skin, from the beginning of the ten days until after he has offered his sacrifice, because the Prophet (peace and blessings of Allaah be upon him) said: "When you see the new moon of Dhu’l-Hijjah, if any one of you wants to offer a sacrifice, then he should stop cutting his hair and nails until he has offered his sacrifice." According to another report he said: "He should not remove (literally, touch) anything from his hair or skin." (reported by Muslim with four isnaads, 13/146)