This is not original, but I did see a Children's Message idea somewhere for this text. The suggestion was that the presenter bring a small branch with dead, dried-up leaves as an object to catch the kids' attention. Ask them if it you could stick this branch in the ground, pour some water on it, and expect it to grow. No … obviously that wouldn't work Why? It's dead. It is cut off from the tree. It has no roots. It has no trunk. And from there, the presenter can get back to our relationship with Jesus. When we are joined with him, we have His nourishment and life. Apart from Him, we are like the dead branch.
I think it is saying that God gave us Jesus so that we could grow through His words, and that if we do as Jesus says we will bear the fruit through His word and be a joy to God and glory in His happiness with us , but if we do not as Jesus teaches, we will be taken loose from our savior so that we cannot corrupt anyone else's growth and take away from any of God's children who are listening to Jesus and bear the fruit of His teachings. Everyone who listens to the words of Christ are following Him and will help teach others, therefore bringing forth more fruit which glorifies God's name even more.