Lingering Damage Health is an alchemical effect in The Elder Scrolls V: Skyrim.
This effect damages the target's Health by a certain amount of points per second, for a certain duration. For example, Orange Dartwing has this effect, it drains the target's Health by 1 point per second for 10 seconds.
One popular combination is to use Imp Stool, Mora Tapinella and Canis Root to make a paralysis poison of lingering damage health. Another is to replace the Canis Root in the above recipe with Deathbell to make a lingering poison of damage health, which deals poison damage over time and also applies an instant damage effect. The most effective combination would though probably be Imp Stool, Crimson Nirnroot and any other ingredient of Lingering Damage Health. With the right perks in Alchemy, and Enchanting for enchanting equipment that boosts your Alchemy skill, the total damage of this poison can be over 500 points (>190 points instant damage, >320 lingering damage). That is more than enough damage to kill a max level Hold Guard with full health, and enough to bring down the health of a Giant with around 85%.