Previously in the gospel of John, Jesus has compared himself to things that were common to the people of his day. He is the good Shepherd, one who cares for his sheep. He is the bread of life, those that come to him shall never hunger. He is the light of the world, those that follow him shall no longer walk in darkness, but will have the light of life.
Grapevines were very common, and in Chapter 15 Jesus presents himself as the true vine, the Saviour, and those who believe in him are the branches. His Father in heaven is the husbandman, over all.
V2 "Every branch in me that beareth not fruit he taketh away: and every branch that beareth fruit, he purgeth it, that it may bring forth more fruit"
There are those who make false professions, but they bear no fruit, there is nothing about them that gives evidence that they are truly saved. These are taken away, either by apostasy or even by death.
On a grape vine, the branches are pruned every year so that they will bear more grapes. If they were allowed to grow freely, there would be very little fruit. Thus it is with Christians, we are chastened to bring forth more fruit. "The trial of your faith worketh patience." Hebrews 12:6 says "For whom the Lord loveth he chasteneth, and scourgeth every son whom he receiveth." These trials are to bring us closer to the Lord. To rely on him to carry us through. With each trial we are strengthened and bear more fruit.
V5, 8 "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.......Herein is my Father glorified, that ye bear much fruit; so shall ye be my disciples."
Christians can do nothing on their own. All that we are, all that we will ever be comes from the Lord as we abide in him. As soon as we try to do something on our own strength, we fail. And when we bear fruit, whether it be sharing the gospel, or witnessing to neighbours or those with whom we are given opportunity, the glory is not ours, the glory is Gods.