Death - the total loss of all Health.
When a hero is slayed by either a monster or another hero, their soul hangs about around their body waiting for a divine helping hand. They still retain their senses and can horrifically smell their bodies rotting and grimly watch the maggots infest them. Their equipment starts to rust and they are able to do nothing but watch in despair. Eventually their body may be discovered and prepared for burial but their god usually has helped them by that time.
After death, a Hero loses all their gold and loot this death is recorded in their death count forever more. Thankfully, quest progress is not reset upon the hero's death, and the god doesn't not lose any godpower.
Pets also are by no means immortal. When a pet dies, nothing happens to the pet or anything else as a result. Unfortunately, resurrection of a pet is much much harder then for a hero so be advised that prevention is the best cure for such problems.
Death is never much of a permanent problem when you have your very own personal god. To find out how bring your hero or pet back to life, see main article.