The image of Israel being the vineyard of the Lord is common in the Hebrews Scriptures. It is in Hosea, Isaiah, Jeremiah and Ezekial as well as often being used by Jesus in the New Testament. Here Jesus identifies himself as the 'true vine.' Clearly he is claiming to be God. In John we look for many levels so we may explore this.
Jesus begins by teaching us of his relationship with his Father. "I am the true vine and my Father is the vinedresser." The Father is the pruner. he cuts off unfruitful branches. he prunes back the fruitful branches so that they be more fruitful.
How does the Father do this? He does it by means of the word that Jesus has spoken to us.
Clearly a branch cannot bear fruit all by itself, but must remain part of the vine. Neither can you bear fruit unless you remain in me. This is because "I am the vine and you are the branches."
Holiness is classically defined as union with God. Holiness means to bear fruit "for cut off from me you can do nothing."
There are so many layers in this passage. It mentions life, growth, fruitfulness, unity plus their opposites. Importance is given to the Word of God, dwelling in Jesus, the power of prayer and the glory of God.
I am the vine and you are the branches. This is one of the many images of Jesus that he has given us of himself. Compare that with the other "I Ams": living water, light of the world, bread of life, resurrection and the life, and the good shepherd. And "I Am" of course is God's name!