Mufti Muhammad Taqi Uthmaani states that the philosophy behind ‘Udhiya’ is that it is a demonstration of total submission to Allah and a proof of complete obedience to Allah’s will or command. When a Muslim offers a ‘Udhiya’ this is exactly what he intends to prove. Thus, the ‘Udhiya’ offered signifies that he is a slave of Allah at his best. And that he would not hesitate even for a moment once he receives an absolute command from his Creator to surrender before it, to obey it willingly, even if it be at the price of his life and possessions.
This is exactly what the Prophet Ibrahim did.