The Bible says after the judgment we who have received Jesus Christ as our Lord and Savior will see eternal life, but those who did not will go and burn forever. I want to know what is that going to burn. Is it the spirit or the flesh?
I don't know that I have an absolute answer for you. There are many places in the Old Testament where the prophets spoke in physical terms but they actually meant something figurative or spiritual. For example, the nature of the kingdom was hidden in such a way that it did not become obvious as to what was being discussed until Jesus and the Apostles explained it in spiritual terms. A good explanation of why it was done that way is because it is hard to explain a spiritual concept and God had to rely on things we understood.
The same can be said about the descriptions of Hell. Jesus says in Mark 9:47-48, "And if your eye causes you to sin, tear it out. It is better for you to enter the kingdom of God with one eye than with two eyes to be thrown into hell, 'where their worm does not die and the fire is not quenched.'" While the scriptures teach it as a place of fire, brimstone and suffering, it is not absolutely certain that such is meant to be the literal description or if it is the best that can be done to describe a spiritual concept to those of us who are stuck thinking in terms of the physical realm. If the descriptions are literal descriptions, then Hell is an absolutely awful place. If it is actually a substitute description, then Hell is even worse than anything we can envision or describe. It is so awful that even God could not come up with adequate words to describe it.
Again, in Revelation 20:10 it says, "and the devil who had deceived them was thrown into the lake of fire and sulfur where the beast and the false prophet were, and they will be tormented day and night forever and ever." It says that the burning is forever. It is hard to misunderstand the length of the time of torment.
So, while it may be interesting from an academic standpoint to know the exact nature of the kind of punishment hell will be, it is not important to understanding our reaction to the place -- none of us want to go there.
I have seen a few writings of people who will try to make a big argument out of the exact nature of Hell. I even saw where someone was trying to prove that Hell could not exist because it says that the flames are never quenched and yet the bodies are supposed to burn forever. His argument was that since bodies have to be consumed in order for a fire to exist, then the description violates a law and that proves the Bible is false. However, what the person failed to appreciate is that we are not told the nature of the afterlife. We don't know the kinds of bodies we will get and we don't know the "rules" of the afterlife. We are confined to a world that has one set of rules. The afterlife doesn't have to have the same rules. Paul says in I Corinthians 15:35-49 that there is a different body in the afterlife. We are told no more than that.
A more important question should be, knowing that there is a Hell and it lasts forever, what should we be doing in order to avoid that place?