Okay, to get the full impact of Jesus’ statement in John 8:58, you have to go back to the Book of Exodus, chapter 3.
This is the story of Moses encountering a bush that is burning but not burning up. Well, technically the encounter was with God who spoke to Moses thru the burning bush. God was calling Moses to lead the Israelites out of their slavery to the Egyptians.
Moses was kind of shy and humble and seemed perfectly satisfied to continue herding sheep. He was not on board with what God wanted him to do and there we read a list of his excuses as to why he thought this was a bad idea.
As part of that conversation, he points out to God that the people might ask what His name is and in Exodus 3:14 God says this: “I AM WHO I AM. This is what you are to say to the Israelites: I AM has sent me to you.”
Back to John 8:58. When Jesus answered the Pharisees, “Truly I tell you, before Abraham was, I am,” He was claiming to be God. To the Pharisees, that was blasphemy, hence the picking up of the stones to throw at Him and kill Him. The problem, however, was the Pharisees’ spiritual blindness.
Jesus really is God.