The Difficulty is a setting for every single Painkiller game where you can choose the game's difficulty to match your skills.
Slumber is the Painkiller: Redemption's easiest difficulty. You start with 200 HP and your health will regenerate back to 200 HP over time if you don't get damaged anymore and every single damage possible is set to take only 1 HP with the exception of death barriers. Also in this mode you will take a lot more ammo from ammo boxes and the Tarot Cards are disabled. Odd enough in this difficulty the demons will not drop souls when they decay but instead you will automatically get in demon form if you reach 50 demons killed but your soul counter will not increase at all because there will be no demon souls to collect. The Mega Souls are useless in this mode because if your health is by any mean different from 200 it will slowly regenerate/degenerate to that value.
Daydream is the easiest difficulty in the whole series with the exception of Painkiller: Redemption which has Slumber. Also in this mode every single damage is set to take only 1 HP with the exception of death barriers and the Tarot Cards are also disabled with the exception of Painkiller: Redemption where they are enabled.
Insomnia is the any casual normal mode which is the way it was meant to be played and you will have an additional level to complete: Factory for Painkiller Heaven's got a Hitman.
Nightmare is a more challenging difficulty where the player will take more damage, less ammo and the checkpoints will not replenish his health and you have to complete the Factory and another additional level: Prison for Painkiller Heaven's got a Hitman. For Painkiller: Battle out of Hell you will have to complete an additional level for it: Pentagon.
Trauma is the hardest difficulty in the whole series where you take even more damage than in Nightmare, even less ammo and you have to complete the previous mentioned additional levels with yet another additional level: The Forest for Painkiller Heaven's got a Hitman. For Painkiller: Battle out of Hell you will have to complete an additional level for it: Pentagon. This mode is the only one where you are not allowed to do quicksaves meaning that if you fail you will have to start all over from the checkpoint. Also every single soul dropped from the monsters are disabled meaning that you have no way of earning HP with the exception of Yellow Soul and Mega Soul.