1. Remain in Jesus and bear fruit (1-4)
Jesus used the analogy of a vine and branches to explain his relationship to believers. He is the true vine. God is the gardener. We are the branches connected to the vine. When a branch doesn't bear fruit, the gardener considers it dead and he cuts it off. This will allow the other branches more nutrients so they will bear more fruit. If we don't bear fruit to God (have faith), we will be cut off. We must remain in the vine (Jesus) in order to bear fruit. We cannot bear fruit on our own.
2. Bear fruit for God's glory (5-8)
Jesus promises that if we remain in him, we will bear much fruit. If we do not remain in Jesus, we can do nothing. We are like a branch that the gardener cuts off and burns. If we do remain in Jesus, we can ask God for anything in Jesus' name, and God will grant it. God wants us to bear much fruit. It is for His glory.