And these will go away into eternal punishment, but the righteous into eternal life.
The doctrine of hell and eternal judgment really is derived from the clear teaching of Jesus. He made it quite clear that He is the Judge of all men, and the parables and teaching in Matthew 25 make this abundantly clear. The fate and destiny of all people hinge on His opinion, and are related to the response each individual has demonstrated to Him and to His people.
Now there is a specific context in Matthew 25. It has to do with "the kingdom" and as such I believe it has to do specifically with the fates of those who will be part of Christ's future millennial reign. But the bit of this that gets my attention has to do with Jesus' insistence that He as the King will determine the eternal fates of those present in this judgment. For those declared righteous, there is eternal life. For those who did not welcome Jesus and care for His "least of these", there is eternal punishment. Heaven and Hell are real fates according to the teaching of Jesus.
There is a growing reluctance to preach this in the current evangelical climate. Two doctrines have crept in to replace Jesus' clear teaching. One view, Universalism, claims that specific faith in Christ, repentance of sin, and a Christian understanding of God will not be necessary to be accepted by God. What matters is sincerity and a commitment to whatever good the person knew. But this is not taught in the Bible, and false religion.... especially ones that promote human works over God's grace, are decried throughout the Bible as insufficient to save. The second usurper is that of Annihilationism, which says that Hell exists, but the soul sent there does not eternally suffer, but instead is destroyed, thus making God somehow more "pleasant" in His role of Judge. Again, this does not square with what Jesus taught specifically about the destiny of those in Hell (see Mark 9:44-48).
So the reality of my life, just as important as the food I eat and the air that I breathe, is that eternal destiny is the fate of every human soul on the planet. It is the first priority for understanding the human need and bettering the world of humanity. It is the first need of my life and should be a driving force for my love for the world.