It is an important ibaadah (worship), and is from among the Sha'aair (symbols) of Islaam. It is not a custom of 'Eid or a source of merry-making and gaiety; but it is a shar'ee (religious) command to renew the commemoration of the Sunnah of Ibraaheem alayhis Salaam and create the spirit and desire of selflessness and sacrifice.
The Qur'aan says:
It is neither their flesh nor their blood, that reaches Allah; it is your piety that reaches him. (22: 37)
Thus, the actual purpose of Qurbaani is to create piety, devotion and a desire for obedience and submission in a human.
Mas'alah: Qurbaani' cannot be offered in the name of anyone besides Allah. It is stated in the Qur'aan:
Lo! My Salaat and my Sacrifice, my living and my dying are for Allah, Lord of the worlds. (6:162)
The History of Qurbaani