Summary: Jesus is the vine and we are the branches
We have looked at Jesus in several ways. Jesus the True Shepherd - John 10: 1 - 6 Jesus the Good Shepherd - John 10: 7 - 18, Jesus the King of Glory - Psalms 24: 7 - 10, Jesus our righteousness - 1 Corinthians 1: 30, Jesus our Stronghold - Psalms 18:2, Jesus The Way, The Truth and The Life - John 14:6, Jesus the Light of the world - John 8:12, Jesus our Redeemer - Matthew 26: 36 - 46, and there are others but today we are going to have a glimpse of Jesus been the True Vine.
John 15: 1 - 8
I am the true vine, and My Father is the vine dresser. Every branch in Me that does not bear fruit He [a]takes away; and every branch that bears fruit He prunes, that it may bear more fruit. You are already clean because of the word which I have spoken to you. Abide in Me, and I in you. As the branch cannot bear fruit of itself, unless it abides in the vine, neither can you, unless you abide in Me.
“I am the vine, you are the branches. He who abides in Me, and I in him, bears much fruit; for without Me you can do nothing. If anyone does not abide in Me, he is cast out as a branch and is withered; and they gather them and throw them into the fire, and they are burned. If you abide in Me, and My words abide in you, you will ask what you desire, and it shall be done for you. By this My Father is glorified, that you bear much fruit; so you will be My disciples.
The amplified version
I am the true Vine, and My Father is the vine dresser. Every branch in Me that does not bear fruit, He takes away; and every branch that continues to bear fruit, He [repeatedly] prunes, so that it will bear more fruit [even richer and finer fruit]. You are already clean because of the word which I have given you [the teachings which I have discussed with you]. Remain in Me, and I [will remain] in you. Just as no branch can bear fruit by itself without remaining in the vine, neither can you [bear fruit, producing evidence of your faith] unless you remain in Me. I am the Vine; you are the branches. The one who remains in Me and I in him bears much fruit, for [otherwise] apart from Me [that is, cut off from vital union with Me] you can do nothing. If anyone does not remain in Me, he is thrown out like a [broken off] branch, and withers and dies; and they gather such branches and throw them into the fire, and they are burned. If you remain in Me and My words remain in you [that is, if we are vitally united and My message lives in your heart], ask whatever you wish and it will be done for you. My Father is glorified and honoured by this, when you bear much fruit, and prove yourselves to be My [true] disciples.
Jesus is speaking to everyone around Him including the disciples. Jesus is explaining to them that He is the vine and His Father is the vine dresser and if we can remember the words of Jesus that always points to His father, He will say to everyone that He only says what His Father says and He only does what his Father does. Jesus was always glorifying His father and depended on His father and not on Himself and this is why He had a successful ministry.
Jesus never did anything outside of His Father's will and purpose. In His time here on earth , He came to fulfil the desire of His Father and He made it known in His ministry that He was sent by His Father and several times God spoke highly of Jesus who came as the True Vine.
Looking at the definition of a Vine in the dictionary. I would say that Jesus is saying that He is a plant or a tree and we as His children are the branches and His Father is the Vine dresser - who does the work of always pruning us as branches so has to bear more fruit to His glory. God will always prune the branches so as to perfect everything for us Son and the WORD actually records to us the love that God as for His Son.
There are scriptures we can refer to about this parable
Jeremiah 18: 1 - 6
The Potter and the Clay
The word which came to Jeremiah from the Lord, saying: “Arise and go down to the potter’s house, and there I will cause you to hear My words.” Then I went down to the potter’s house, and there he was, making something at the wheel. And the vessel that he made of clay was marred in the hand of the potter; so he made it again into another vessel, as it seemed good to the potter to make.