As with the other "I am" statements in the gospel of John, Jesus' words "I am the vine" not only claim He is the great Jehovah ("I am Who I am") but also describe one of His roles as God within the Godhead that is the trinity.
Jesus is with the apostles in the upper room during the last supper. He had already told them "I am the way, the truth, and the life" (John 14:6), an unmistakable claim of deity. When Jesus adds "I am the true vine, and my Father is the vinedresser" (John 15:1) He was then clarifying His and His Father's roles in the lives of those who worship the true God. Both He and the Father perform duties the Old Testament had already made clear were unique to God. As "the true vine" Jesus is claiming to be the source of life, like the grape vine that shoots out from the ground. Yet, Deuteronomy 32:39 affirms of God "See now that I, even I, am he, and there is no god with me: I kill, and I make alive; I wound, and I heal: neither is there any that can deliver out of my hand."
Abraham, through successful completion of God's greatest test, came to know God as "Jehovah Jireh," the "I am" Who provides (Gen. 22:14). Jesus asserts here that He alone is the source of all life, spiritual or physical, and provides not only the path to His Father but also the ability to walk it. The Father Himself is not the root, the source of life to the vine, but the "vinedresser," the One Who prunes the vines. This picture, a little obscure today, would have been readily understood by anyone in that day. Even people who did not work with grapes knew the principle of pruning: a branch that has born fruit one year, will not again bear fruit. A vine unpruned of its branches will in time grow no fruit, eventually not even any leaves. Inside that branch may or may not be sap from the root, but any present sap would not be manifest in the life of the vine (unless one were to cut it off and look at the middle.)
Thus Jesus goes on to say ...