The Goal of the Udhiyyah (Sacrifice) according to Allah is the Sincerity and Taqwa of His Servant
” It is neither their meat nor their blood that reaches Allah, but it is Taqwa from you that reaches Him. Thus have We made them subject to you that you may proclaim Allah’s greatness for His guidance to you. And give glad tidings to the doers of good.”[Surah Hajj: 37]
Allah says: this sacrifice is prescribed for you so that you will remember Him at the time of slaughter, for He is the Creator and Provider. Nothing of its flesh or blood reaches Him, for He has no need of anything other than Himself. During the time of Jahiliyyah, when they offered sacrifices to their gods, they would put some of the meat of their sacrifices on their idols, and sprinkle the blood over them.
But Allah says: (It is neither their meat nor their blood that reaches Allah,) Ibn Abi Hatim recorded that Ibn Jurayj said, “The people of the Jahiliyyah used to put the meat of their sacrifices and sprinkle the blood on the House, and the Companions of the Messenger of Allah said, “We have more right to do that.”
Then Allah revealed the words:
(It is neither their meat nor their blood that reaches Allah, but it is Taqwa from you that reaches Him.) That is what He will accept and reward for, as mentioned in the Sahih,(Allah does not look to your appearance or your colors, but He looks to your hearts and deeds.)
And in the Hadith; ”Indeed charity falls in the Hand of Ar-Rahman before it falls in the hand of the one asking.”
(Thus have We made them subject to you) meaning,`for this purpose We have subjugated the Budn for you,
‘ (that you may proclaim Allah’s greatness for His guidance to you.) means, that you may glorify Him for guiding you to His religion and His way which He loves and is pleased with, and has forbidden you to do all that He hates and rejects.
(And give glad tidings to the doers of good.) means,`give good news, O Muhammad, to those who do good,’ i.e., whose deeds are good and who remain within the limits prescribed by Allah, who follow that which has been prescribed for them, who believe in the Messenger and follow that which he has conveyed from his Lord.
(Note) The Udhiyyah is Sunnah Mustahabbah One animal is sufficient on behalf of all the members of one household. Ibn `Umar said, “The Messenger of Allah continued to offer sacrifice for ten years.” This was recorded by At-Tirmidhi. Abu Ayyub said: “At the time of the Messenger of Allah , a man would sacrifice a sheep on behalf of himself and all the members of his household, and they would eat from it and feed others, until the people started boasting ﴿by sacrificing more than one﴾ and things reached the stage that you see now.” This was recorded by At-Tirmidhi, who graded it Sahih, and by Ibn Majah. `Abdullah bin Hisham used to sacrifice one sheep on behalf of his entire family; this was recorded by Al-Bukhari. Concerning how old the sacrificial animal should be, Muslim recorded from Jabir that the Messenger of Allah said:“Do not slaughter any animal except for one that is mature in age unless that is difficult for you, in which case you may slaughter”
Source: Tafsir of Al-Hajj : 37 taken from: Tafsir Ibn Kathir