Q: What is the Uḍḥiyyah and what is its ruling?
A: Uḍḥiyyah is either a camel, cow, sheep, or goat which is slaughtered during the days of sacrifice i.e. the day of Eid and the following two days due to the Eid as an act of devotion (qurbah) to Allāh.
According to consensus it is a legislated act based on Allāh’s statement, “So pray to your Lord and sacrifice [to Him alone]” (al-Kawthar 108:2). A number of tafsir scholars have interpreted this verse to mean the slaughter that occurs after the Eid prayer. It has also been authentically reported as a prophetic practice.
It’s mentioned in Sahih al-Bukhari and Muslim, that “The Prophet (ﷺ) slaughtered two rams, black and white in color (as sacrifices), and I saw him putting his foot on their sides and mentioning Allah's Name and Takbir (Allahu Akbar). Then he slaughtered them with his own hands”.
It is a stressed sunnah.
Source: Sharh al-Muntaha