Regen delay is the number of turns it takes a creature to regenerate 1 health. Creatures with a regen delay of 0 (such as jellies, zombies and golems) do not regenerate at all.
Monsters and allies have a set regen delay that never changes. Your regen delay is dynamically adjusted so that you can regenerate all of your health in 300 turns. This number can be reduced by equipping a ring of regeneration.