R.C. Sproul’s answer may surprise you:
It is common to say that hell is the absence of God. Such statements are motivated in large part by the dread of even contemplating what hell is like. We try often to soften that blow and find a euphemism to skirt around it.
We need to realize that those who are in hell desire nothing more than the absence of God. They didn’t want to be in God’s presence during their earthly lives, and they certainly don’t want Him near when they’re in hell. The worst thing about hell is the presence of God there.
When we use the imagery of the Old Testament in an attempt to understand the forsakenness of the lost, we are not speaking of the idea of the departure of God or the absence of God in the sense that He ceases to be omnipresent. Rather, it’s a way of describing the withdrawal of God in terms of His redemptive blessing.
It is the absence of the light of His countenance. It is the presence of the frown of His countenance.
It is the absence of the blessedness of His unveiled glory that is a delight to the souls of those who love Him, but it is the presence of the darkness of judgment.
Hell reflects the presence of God in His mode of judgment, in His exercise of wrath, and that’s what everyone would like to escape.
I think that’s why we get confused. There is withdrawal in terms of the blessing of the radical nearness of God. His benefits can be removed far from us, and that’s what this language is calling attention to.
—R. C. Sproul, The Truth of the Cross (Orlando, FL: Reformation Trust, 2007), pp. 157-158; my emphasis.