Reduction in health or an action that reduces health from an attack. For example, a weapon attack or spell attack that reduces the health of the target is damage, but losing a health boosting buff is not considered damage.
Losing mana from an attack can also be considered damage, but generally is not referred to in that way, since reducing mana to 0 (zero) won't cause death; nor do mana-drain only spells interrupt casting or other actions prone to damage, such as bandaging.