The vine was a symbol of Israel — God's planting, meant to bear fruit — and the prophets grieved when it produced only wild grapes. Into that long story Jesus spoke: I am the true vine. He is what Israel was meant to be, and the source of all real fruitfulness. The branch bears fruit only by staying joined to the vine.
The lesson is dependence: he that abideth in me, and I in him, the same bringeth forth much fruit: for without me ye can do nothing. Fruit is not manufactured by effort but grown by connection — abide in Christ, and the sap of his life produces love, joy, peace, and every grace. The vine also gives wine, the cup of the new covenant: from union with Christ flows both fruitfulness and joy.
The Vine in Scripture
I am the vine, ye are the branches: He that abideth in me, and I in him, the same bringeth forth much fruit: for without me ye can do nothing.