The Prophet was asked about animal sacrifice. He replied: سُنَّةُ أَبِيكُمْ إِبْرَاهِيمَ (Sunan Ibn Majah 3127) This is the practice of your forefather Ibrahim. Hazarat Ibrahim was commanded in a dream to sacrifice his son Ismail. In the dream, Prophet Ibrahim saw that he was sacrificing his son. He thought in reality he should sacrifice his son, and got ready for this. Then God Almighty commanded him to not sacrifice his son. He was instructed to sacrifice a ram where he had planned to sacrifice his son. Then Prophet Ibrahim sacrificed a ram in place of his son. This has been called in the Quran as وَفَدَيْنَاهُ بِذِبْحٍ عَظِيمٍ (37.107) We ransomed him with a great sacrifice.

Here zibh-e-azeem means a great sacrifice. This implies that there must also be zibh-e-sagheer. If there is zibh-e-azeem, there must also be zibh-e-sagheer, or lesser sacrifice. What is the great sacrifice? This was settling his son Ismail in the desert. There a team was prepared. The lesser sacrifice was the sacrifice of the ram. Hazarat Ibrahim's sunnah is that the lesser sacrifice isn't all that important. It is the great sacrifice that is important: to dedicate oneself to and to offer oneself for the cause of truth. He presented his son for the cause of truth and the animal sacrifice was done as ransom for his son.  On the day of Hajj and Eid al-Adha, our animal sacrifice is the lesser sacrifice. It is not the great sacrifice. The animal is sacrificed as ransom. When we sacrifice an animal, we pledge that we will dedicate ourselves to God's cause. Sacrifice doesn’t mean to kill yourself. Sacrifice means to dedicate yourself to God's cause. To dedicate yourself fully to  God's cause. This is the sacrifice. The animial Hazarat Ibrahim had sacrificed in place of Ismail was the lesser sacrifice. Settling Ismail and his mother Hajara in the desert to prepare a team, was a the great sacrifice.