If you have ever done any sort of gardening in your life, then you know how important it is for many kind of flowering bushes to be trimmed occasionally, or pruned. Pruning a shrub by cutting off the dead branches and flowers not only keeps the shrub looking better, but makes it a healthier plant. Many times, a particular branch might die due to some disease or fungus, and so removing these dead branches keeps the disease from affecting the rest of the plant, or it may promote growth simply by allowing more sunlight to reach the healthier branches underneath.
Jesus talks about this exact thing in John 15:5-8, "I am the vine; you are the branches. If you remain in me and I in you, you will bear much fruit; apart from me you can do nothing. If you do not remain in me, you are like a branch that is thrown away and withers; such branches are picked up, thrown into the fire, and burned. If you remain in me, and my words remain in you, ask whatever you wish, and it will be done for you. This is to my Father's glory, that you bear much fruit, showing yourselves to be my disciples."
So what is Jesus saying here? Let's start with the first line. Jesus says that he is the vine, and we are only the branches. The only reason the branches live is because the vine lives. If at any moment the vine dies, then the rest of the plant dies. All its leaves, flowers, fruit, and branches die with the vine. But here we have Jesus saying that he is the vine, declaring that the vine is alive and producing fruit, creating more branches, and constantly growing, as a healthy, living plant does. Jesus is alive, so much more so than we can fully appreciate! And he is not only alive, but he has in fact defeated death itself, so that he will never again face death! And so if we are the branches of a vine that will never die, then we also will never die! Going on, Jesus says promises us that if we remain in Him, he will remain in us. It is the promise of life described exactly by what he said previously; He is the undying Vine, and he will never cut a living branch away from himself. That is, as long as we are living for Him, he will never leave us, and we will inherit eternal life from Him, because we are an inseparable part of Him now. And that is a promise. Jesus is always with us, and He alone gives us life. There is nothing else is the world that can give us the life that Jesus offers us, because His is the only vine that is alive and that will never die. "Grass withers, and flowers fade, but the word of our God stands forever."
So then what does it look like for someone who is not bound to Christ? They die. Everyone dies, but not everyone truly lives. Everyone dies, but the faithful will live on. So what happened to those that died? They must not have been a part of the Vine of Jesus. Because Jesus promises us that if we are in Him, he is in us and will never leave us, then any branch that is a part of him cannot die; He simply will not allow it. But any branch that is a part of any other plant cannot live forever, and will eventually die. It is just hard to imagine someone who believes that they are a member of Jesus' vine, when in fact they are growing out of a dying plant nearby. And they may not even realize that they are not truly living for Christ; they are surrounded by Christians, maybe even trying to do good and live a holy life, but if they are holding onto any anchor other than Christ, then they are not one of the branches being supplied with the life of Jesus. This is a harsh truth, but I fully believe that not everyone who claims to be a Christian actually is, because being a Christian is so much more than simply saying "I believe," but being a Christian is about knowing Jesus and having a deep, intimate relationship with Him. In Matthew 7:21-23, Jesus says this quite clearly: "Not everyone who says to me, 'Lord, Lord,' will enter the kingdom of heaven, but only the one who does the will of my Father, who is in heaven. Many will say to me on that day, 'Lord, Lord, did we not prophesy in your name and drive out demons and in your name perform many miracles?' Then I will tell them plainly, 'I never knew you. Away from me you evildoers!' ". So many people might look at the passage in John and talk of the dying branches as believers who have lost faith, and therefore lost salvation. But looking at this passage in Matthew, I would say that these 'believers' were never saved in the first place. And so what happens afterward is only the promise of our Father, that if we are not saved by the blood of Jesus, having been washed with His righteousness through faith alone in Him, then we cannot be allowed into heaven, and instead will be punished rightly for our sin through an eternity in Hell.
Moving on, we see a verse that sounds right at home in a prosperity Gospel. "[A]sk whatever you wish, and it will be done for you." So that means that God will make me rich if I ask Him, right? He will provide me with a good job, a beautiful wife, obedient children, and a safe, comfortable life in the suburbs with a white picket fence out front. We see a similar verse in Psalm 37:4, "Take delight in the Lord, and he will give you the desires of your heart." But the problem is that the desires of our heart are, by nature, sinful. We seek the fleeting pleasures of this life in sex, alcohol, drugs, money, popularity, any many other things, believing that they will give us lasting joy. But they never do, and they never will, because these things are not capable of bringing us joy. Joy is something that comes from the Lord, as we are told over, and over again throughout the Bible, "Rejoice in the Lord!". The sinful things of this world may bring happiness, but they can never bring us joy, and so what makes us think that God would give us something so petty as money? Our Father is a God who gives good gifts to his children so that we may love him more, so when we are told that we will be given what we ask, Jesus is really saying that he will give us what we ask if we rejoice in the Lord, such that what we are asking for is more joy. Joy comes from the Father, and He wants us to live in the fullness of joy, simply overflowing with it, so of course He will give us more joy if we ask. He will give us the Holy Spirit if we ask. And he will give us life if we ask. It is as simple as that. So when we see that "This is to my Father's glory" that we are given what we ask, it is so that we can be given much joy so "you bear much fruit", and in bearing the fruit of Jesus, we will be "showing [ourselves] to be [Jesus'] disciples.". It is that simple. Jesus offers us life so that we may live in it, "growing up in our salvation, now that we have tasted that the Lord is good.", so that through Him supplying us with the fullness of life, we may bear such fruit that we graft other's into the vine of Jesus, who heals their diseases and changes their lives so that they too may bear fruit. This is the picture of the Church, of what we as Christians are offered, and what we are called to. Apart from Him, we can do nothing, but with Him, nothing is impossible, because our God is a God of the impossible.