Hell is indeed an eternal state of existence. It is to exist eternally outside of God’s presence and love.
The teaching of the Church affirms the existence of hell and its eternity. Immediately after death the souls of those who die in a state of mortal sin descend into hell, where they suffer the punishments of hell, “eternal fire.” The chief punishment of hell is eternal separation from God, in whom alone man can possess the life and happiness for which he was created and for which he longs. (Catechism, 1035)
I’m not sure we can say that hell is about “deserving” to be there. Hell is the result of a free choice to reject God. God respects our free will and if, by our actions and choices, we reject him, he will not force himself upon us. While we might say no one “deserves” eternal hell, if they choose to reject God that is the consequence of that choice.
This rejection of God is referred to as mortal sin. To be culpable of a mortal sin the individual must freely choose what he truly knows to be gravely wrong. By such a choice a person explicitly rejects a relationship with God who is love. Even heaven would be hell for such a person. Imagine not desiring the things of God and then having to spend all eternity surrounded by them? It is “hell” for such a person either in heaven or in hell.
Understanding heaven, hell, judgment, sin and redemption are a bit of a mystery. While we can use our reason and judgment, our experience is only on this side of reality and thus limited. Ultimately we need to trust that God is truly loving, merciful, and just, and that he desires all to be saved (1 Tim. 2:4; 2 Pet. 3:9). Anyone who ends up in hell ends up there because of their own choice and not the action of God (Matt. 23:37).