Damage absorption is a trait that allows a creature to regain hit points instead of taking damage from a specific damage type. Typically, the creature is immune to the damage type, and also has a trait noting that. You can see how it is written on the Flesh Golem in the Basic Rules below:
As you can see, the golem is immune to lightning damage. It also has a trait that allows it to heal when it would take lightning damage. Other creatures have the same feature with different damage types.
Monsters with Damage Absorption:
You can find lists of monsters with other exciting abilities here.