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As with all analogies, Jesus' analogy of the vine and branches is imperfect, as grape vines and vinedressers are not wholly analogous to a believer's relationship with Jesus and the Father. Yet Jesus obviously saw some characteristics of grape vines and vinedressers that served well to illustrate some important spiritual truths. We only need to be cautious that we don't "push the parable too far."
It seems safe to assume that only believers are comparable to branches in Jesus' vine, as only those "in Christ" can bear fruit that stems from "abiding in the vine." Jesus, of course, was not speaking to unbelievers, but to His closest disciples, telling them that they were the branches.
Just like a vinedresser, the Father wants to see fruit on the branches. Those that are bearing fruit, He prunes, cutting away what is undesirable to Him in order that the branch might bear more fruit. That is God at work in the process of sanctification.
Those that are not bearing fruit, He cuts off. Because this is a metaphor, we can't be entirely sure if this "cutting off" speaks of the judgment of physical death in which a believer still maintains his eternal salvation, or if it speaks of a forfeiture of salvation all together. Of course, Jesus exhorted His closest disciples to "abide in [Him]" (15:4) that they might bear fruit, and then went on to warn them, "If anyone does not abide in Me, he is thrown away as a branch, and dries up; and they gather them, and cast them into the fire, and they are burned" (15:6). This certainly sounds like a warning of hell, and if the branch that removes itself becomes fruitless and is cast into hell, it would seem odd that a fruitless branch that is removed by the Father would inherit eternal life.
In any case, after reading John 15, no one can argue that our bearing fruit is a trivial matter to God. The reason He chose and appointed us was so that we could "bear fruit," and so our "fruit would remain" (15:16).
Take note of the role of prayer in the matter of bearing fruit. Jesus promised:
If you abide in Me, and My words abide in you, ask whatever you wish, and it shall be done for you. By this is My Father glorified, that you bear much fruit, and so prove to be My disciples" (15:7-8; see also 15:16).
When Jesus encouraged His disciples to "ask whatever they wished," He wasn't thinking that they would be asking for material treasures to lay up on earth, as that would indicate that they were not abiding in Him and His words were not abiding in them. Jesus was thinking that their supreme desire would be holiness, and so His encouragement to "ask whatever they wished" was supposed to encourage them to pray for what would make them more fruitful. God always answers those kinds of prayers!
Jesus' words, "If you keep My commandments, you will abide in My love," does not sounds like a promise of "unconditional love" that is so often touted in Christian circles, but of conditional love, and so it is. God loves everyone conditionally. We are Jesus' friends if we do what He commands us (15:14). If God loved everyone unconditionally, then no one would be ultimately cast into hell. What many refer to as "God's unconditional love," would be better termed, "God's temporary mercy." God loves everyone with a merciful love, but that is temporary for those who don't repent.
True Christians are loved and hated---loved by each other and hated by the world. How strange and confusing it can be to find yourself hated by "Christians!" Take comfort knowing that Christians who hate Christians aren't Christians. (You can quote me on that.) "Christians" who hate Christians are every bit as deceived as the scribes and Pharisees of Jesus' day who professed to love God but hated Jesus (15:23-24). This was also greatly emphasized in John's first epistle, where he repeatedly told his readers that love for each other is a litmus test of genuine faith in Jesus. Heaven is for lovers!