What did Jesus mean when He declared, “I tell you the truth, before Abraham was even born, I AM!” ? (John 8:58)
"This famous verse, I believe, can only receive one honest interpretation. It is a distinct assertion of our Lord’s eternity - His existence before all creation. Let us carefully note what a strong proof we have here of the pre-existence and Divinity of our Lord Jesus Christ. He applies to Himself the very name by which God made Himself known when He undertook to redeem Israel. It was “I AM” who brought them out of the land of Egypt. It was “I AM” who died for us on the cross. The amazing strength of the foundation of a sinner’s hope appears here. Believing on Jesus we rest on Divinity, on One who is God as well as man."
From: Expository Thoughts J.C. Ryle, 2:132
“I AM WHO I AM” are allusions to the eternality of God. No mere human being can make a comparable claim. All humans have come into existence. But not God. God is eternal in nature and infinite in Divine essence— with no beginning and no end. It is this identity and these essential qualities Jesus Christ claimed to possess; being equal to and intrinsically, God Himself.