Qurbani is one of the rites carried out during Hajj and Eid ul-Adha. It is a sunnah from the prophet Ibrahim (as) and his son, Prophet Ismail (as). Qurbani is carried out by many millions of Muslims across the world.
Prophet Ibrahim (as) had a dream in which he saw that he was sacrificing his son Ismail (as). He went to Ismail (as) and informed him of his dream, who replied;
"O my father! Do that which you are commanded InshAllah (if Allah wills), you shall find me of the patient."
So Prophet Ibrahim (as) proceeded to sacrifice his son Ismail (as). However, when Ismail (as) was laid ready for the sacrifice, Allah (swt) called to Prophet Ibrahim (as) and said;
"O Abraham! You have fulfilled the vision. Indeed, We thus reward the doers of good. Indeed, this was the clear trial. And We ransomed him with great sacrifice. And we left for him [favourable mention] among later generations. Peace be upon Abraham. Indeed, We thus reward the doers of good. Indeed, He was of Our believing servants." (Ch37:99-111 Quran)
So, having fulfilled the dream and showing complete obedience to Allah, Prophet Ibrahim (as) sacrificed a sheep instead. This is the sunnah that all Muslims now follow during the time of Hajj.