First, notice the setting to which they refer—when Jesus "comes in His glory" (Matthew 25:31-32). We are told that He separates the sheep from the goats. The sheep represent the righteous (Matthew 25:34-40). At His return He sets the sheep at His right hand. The goats in this instance represent sinners. They are appointed to assemble on Jesus' left hand. He then consigns the goats to "the everlasting fire prepared for the devil and his angels" (Matthew 25:41).
The word everlasting is translated from the Greek word aionios. The key to understanding this verse is knowing what will occur everlastingly. Does it refer to a fire that tortures without end, or does it have another meaning?
In Matthew 25:46 Jesus spoke in a single sentence of everlasting (aionios) punishment and of life eternal (aionios). Since the righteous will be given eternal, or everlasting, life, many theologians believe the punishing of the wicked must last as long as the life given to the righteous. But this cannot be reconciled with the statement that those cast into the lake of fire perish—they are killed. As explained elsewhere, they suffer death—the second death (Revelation 2:11; Revelation 20:6, Revelation 14:1-20; Revelation 21:8).
A plain and simple meaning of Matthew 25:46 that fits with the rest of the Bible is that the wicked are cast into a fire that annihilates them—renders them forever extinct. The resulting punishment of being cast into the aionios fire is a one-time event. It is a permanent punishment, the results of which will remain forever—that is, eternal death. It is not ongoing punishing that continues forever without end. This is the only explanation that agrees with the rest of the Scriptures.
An additional point needs to be made regarding the meaning of aionios. Genesis 19 describes God's destruction of two cities, Sodom and Gomorrah, for their wickedness: "Then the LORD rained brimstone and fire on Sodom and Gomorrah" (Genesis 19:24). They were utterly destroyed—consumed by fire.
In the New Testament, the book of Jude describes these cities as "suffering the vengeance of eternal [aionios] fire" (Jude 1:7). Yet it is obvious that the fires that destroyed Sodom and Gomorrah are not still burning. In the case of these cities and in the case of the wicked, who are consigned to aionios fire, the fire burns and completely destroys. But the eternal aspect of the fire is its everlasting effect, not how long it actually burns.