Question: "What did Jesus mean when He said 'I AM'?"
Jesus, in response to the Pharisees’ question “Who do you think you are?” said “‘Your father Abraham rejoiced at the thought of seeing my day; he saw it and was glad.’‘You are not yet fifty years old,’ the Jews said to him, ‘and you have seen Abraham!’ ‘I tell you the truth,’ Jesus answered, ‘before Abraham was born, I am!’ At this, they picked up stones to stone him, but Jesus hid himself, slipping away from the temple grounds.” The violent response of the Jews to Jesus’ “I AM” statement indicates they clearly understood what He was declaring—that He was the eternal, incarnate God. Jesus was equating Himself with the "I AM" title God gave Himself in Exodus 3:14.
If Jesus had merely wanted to say He existed before Abraham’s time, He would have said, “Before Abraham, I was.” The Greek words translated “was” in the case of Abraham, and “am” in the case of Jesus, are quite different. The words chosen by the Spirit make it clear that Abraham was “brought into being,” but Jesus existed eternally (see John 1:1). There is no doubt that the Jews understood what He was saying because they took up stones to kill Him for making Himself equal with God (John 5:18). Such a statement, if not true, was blasphemy and the punishment ascribed by the Mosaic Law was death (Leviticus 24:11-14). But Jesus committed no blasphemy; He was and is God, the second Person of the Godhead, equal to the Father in every way.