Here is what I believe about hell, SO. I posted it before somewhere else.
Catholics and the Orthodox, following the teachings of the earliest Christians, believe that it is impossible for God not to love us, his earthly children. Love is his very essence and he made us expressly so that he could love us. God loves us so much that he sent his only-begotten son to save us and demonstrate the length he would go to to show us he loves us.
Out of love for us, he made us in such a way that our deepest longings, our most profound needs, are satisfied in Him. He made us to find our fulfillment in the best he had, Himself. He made us to be his lovers; thus we will never be satisfied until we are in perfect relationship with him. When that happens, we will also be in the correct relationship with all other creatures who are in relationship with him, a huge loving family of giving and shared experiences. That is why he made us, so that he could love us and share his life with us.
Love, by its very nature, must be spontaneous. It cannot be forced or coerced and still be love. In order to meet that condition, God had to give us free will, along with the qualities of character we would need to exercise that free will, including intelligence, curiosity, and the capacity for faith and love. As a consequence, we must make a free choice to obey God; we must come to him in pure loving response to what he has done for us. God would never try to force us into obeying him, even though He knows we will never be completely happy until we conform our thoughts and actions to His.
But free will also has a corollary. Since we have the God-given capacity for choice, He must also give us the right to reject Him. If that were not true, we would not truly have free will. If we choose to go down that path away from our Creator, God will use every means at his disposal, short of violating our free will, to call us to repentance. He offers free forgiveness and He demonstrates his love for us over and over again, in hope that we might come to realize that only in full, complete relationship with him will we ever realize our potential as his children, made in his own image. But ultimately, we have the right to reject him, even to hate him, to substitute love we ought to have for Him and give it to other, lesser things.
In the words of C.S. Lewis on this subject, it boils down to this: "In the end, we either say to God: 'Thy will be done' or God will say to us 'Thy will be done.'" God knows (because he made us) that once we get to that point, despite all his efforts to demonstrate his love for us, that our hatred will grow until we hate Him with all our heart (just as Satan does). Those who ultimately will end up hating God will seek to be away from his presence, even if they would be welcome there.
So as a final act of love for them, he provides them a place where they can be shielded from his love and light, which otherwise permeates all existence. God will abandon such creatures to their own devices. They will be in what Jesus called "outer darkness". Just "where" that will be is not the point at all. Even if God were to allow such people full access to his presence , they would hate to be there. Like a Rock & Roll fan at an opera, or an opera fan at a Heavy Metal concert, the same "place", God’s presence, would be heaven for one and hell for the other. Imagery like fire is used in Scripture to represent the pain of separation from God (which is the Catholic definition of hell, by the way).(BTW, some Christian mystics have suggested that heaven and hell are the same place, that only the perception of the individual makes them different.)
A clarification about eternity. Eternity does not mean an endless succession of days; millions, billions or trillions of them. Eternity means being outside of time, timeless (that is the literal meaning of the word). All of our linear, sequential time is included in timelessness. One way to envision that is to think about the relationship of our linear time to the "time" in storybooks on a shelf. We can open a book and enter a particular "time", the succession of events found in that story. Then we can close the book and be completely outside of that "time", then later reopen it and be right back in it. That is how some orthodox thinkers have compared the linear time we live in to the eternity in which God dwells. It is mysterious but not impossible to imagine.
Those who reject God will end up living in timelessness also, but without the one thing they need to be happy: God. But it will be their own choice about the matter. They will not just be sent somewhere because they inadvertently broke some little rule or other. It will be because they have made a fully informed choice, of their own free will, knowing full well the consequences of their choice, to live without God, and, when offered the chance to change their mind and repent, will refuse. Those who do that will be, completely as a result of their own choice, in hell.
I would recommend C.S. Lewis' "The Great Divorce" for a more complete (and much better) exploration of this subject, which was also very difficult for Lewis. It was very helpful to me.
Tom