In the spring, vines often produce flowers. Some vines produce fruit or vegetables. If you look at the same vines in the winter season, however, it often looks like there is no growth. It's essential for the vine to stay connected in the the down times of growth to maintain a constant source of nurtrition for the spring. Once cut, the vines will not flourish. The joint must not be broken.
With Jesus' words recorded in John, He was giving the disciples a word picture about spiritual growth. Jesus is the Vine, our Life source. Our Only Source. We, as believers, are the branches. It is essential to stay connected to our only source of Life. If we remove ourselves, we will not bear fruit, we will not grow, we will shrivel. Jesus gives life, maintains growth and bears fruit in us IF we remain connected to Him. We must stay grafted to Jesus. Jesus must remain our source of life. Without him we will shrivel, dry up and be unproductive.
We are not designed to do this life alone. You have heard of the saying "a God-sized hole" in your heart, I believe that to be true. Part of God's intimate design for each of us is a need that can only be filled by him. So when we try to fill our lives with everything but God, we will get a false sense of security and satisfaction. No one wants that!