At the day of judgement they will receive the fearful and just sentence of condemnation pronounced against them. They will be cast out from the favourable presence of God, into Hell, to be justly and grievously punished, forever.
“For God so loved the world that He gave His one and only Son, that whoever believes in Him shall not perish but have eternal life. For God did not send His Son into the world to condemn the world, but to save the world through Him. Whoever believes in Him is not condemned, but whoever does not believe stands condemned already because they have not believed in the name of God’s one and only Son… Whoever believes in the Son has eternal life, but whoever rejects the Son will not see life, for God’s wrath remains on them.” (John 3:16-18,36)
There are fundamentally only two kinds of people: those who submit to God and those who rebel against Him.
Whoever does not believe is condemned
On the Day of Judgement, when Jesus returns as King and Judge, those who have rejected Him in life will be unable to bear the presence and glory of God. They will be forced out of His presence (and therefore excluded from all love, hope, light and joy) for ever (II Thessalonians 1:8-10). This will be what we call Hell.
Jesus made many references to Hell in His teaching. Some times He spoke of it as like an eternal fire of destruction (e.g. Mark 9:43-48; Matthew 25:41), sometimes as like being shut out of the most fantastic party ever thrown (e.g. Luke 13:24-28; Matthew 25:30). Obviously these are metaphors, but the message is clear: Hell is a state of utter agony and despair.
Whoever believes in the Son shall not perish
Perhaps the worst thing about Hell is that it is completely unnecessary for anyone to go there. For Jesus “rescues us from the coming wrath.” (I Thessalonians 1:10) While Jesus was on the cross, He suffered much more than physical pain. “At noon, darkness came over the whole land until three in the afternoon. And at three in the afternoon Jesus cried out in a loud voice, ‘Eloi, Eloi, lama sabachthani?’ (which means ‘My God, my God, why have You forsaken me?’)” (Mark 15:33,34) His cry expressed not only terror of God’s wrath, but also the nightmare of desolation and abandonment that is the essence of Hell. He endured all the horror and agony of separation from God – so that we need never experience it.
Praise the Lord, my soul; all my inmost being, praise His holy name. Praise the Lord, my soul, and forget not all His benefits – who forgives all your sins and heals all your diseases, who redeems your life from the pit and crowns you with love and compassion. (Psalm 103:1-4)