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The repeated Qur'anic insistence on pronouncing the name of God whenever one slaughters an animal is meant to make the believers "realize the awfulness of taking life, and the solemn nature of the trust which God has conferred upon them in the permission to eat the flesh of animals" (Marmaduke Pickthall, The Meaning of the Glorious Koran, London 1930, p. 342, footnote 2). As regards the "days appointed" (ayyam ma 'lumat) spoken of above, they apparently denote the Festival of Sacrifices, which falls on the 10th of the lunar month of Dhu 'l-Hijjah, as well as the nest two days, marking the end of the pilgramage (Ibn 'Abbas, as quoted by Razi).
Lit., "that they might witness benefits [accruing] to them" - i.e., increased consciousness of God through facing the first temple ever dedicated to Him, as well as the consciousness of being part of a brotherhood embracing all believers. Apart from these spiritual benefits, the annual pilgrimage to Mecca provides an opportunity for believers from all parts of the world to become acquainted with the many social and political problems that confront various geographically separated sectors of the community.
Whereas the pilgrims are merely permitted to eat some of the flesh of the animals which they have sacrificed, the feeding of the poor is mandatory (Tabari and Zamakhshari) and constitutes, thus, the primary objective of these sacrifices. Apart from this, they are meant to commemorate Abraham’s readiness to sacrifice his first-born son after he dreamt that God demanded of him this supreme sacrifice (see {37:102-107} and the corresponding notes); furthermore, they are a reminder that God is the Provider of all sustenance and the One who gives life and deals death, and that all must return to Him; and, lastly (as stressed by Razi), they are to be symbols of each believer’s readiness to sacrifice himself in the cause of truth.
Spiritual benefits such as prayers, pilgrimage, and forgiveness of sins, as well as worldly benefits such as meeting Muslims from everywhere and trading.
There are benefits both for this our material life and for our spiritual life. Of the former kind are those associated with social intercourse which furthers trade and increases knowledge. Of the latter kind are the opportunities of realising some of our spiritual yearnings in sacred associations that go back to the most ancient times. Of both kinds may be considered the opportunities which the Pilgrimage provides for strengthening our international Brotherhood.
The three special days of Hajj are the 8th, 9th, and 10th of the month of Zul- hijjah, and the two or three subsequent days of Tashriq: see the rites explained in n. 217 to ii. 197. But we may ordinarily include the first ten days of Zul-hijjah in the term.
The great day of commemorative Sacrifice ('Id-ul-Adhha) is the 10th of Zul- hijjah: the meat then killed is meant to be eaten for food and distributed to the poor and needy.