Max Health, often abbreviated as HP for Hit Points, defines how much damage the Hero can take. It's the number of Hit Points the hero has when they are uninjured. In this case, the Health Bar is full and green because it reflects 100% health.
Current Health is the green part of the health bar and a percentage of Max Health. Injuries are the red part of the health bar. Any damage reduces the Current Health. 1 damage causes 1 hit point to be lost. There are also some Effects and Special Attacks that cause 
Health Loss and reduce the Current Health by a percentage.
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If the current health is 0, the hero is dead. That's pretty bad, Boss! |
To contiune the fight with a dead hero, you must revive the fallen hero, otherwise they won't be of much help. Only very few Heroes have the power to overcome death. See 
Resurrection for details.
The 
Unbreakable Heart buff, the Trait with the same name that 
Icebloom has and that is added by Runes, and some some other buffs like 
Ethereal Spirit, can keep the Current Health at 1 regardless of the damage dealt. Usually, this works only once in the Raid or the dungeon run.
Current Health can be restored by 
Heal, 
Lifesteal, or 
Regeneration. Constructs, except 
Living Stone constructs, cannot be healed. They must be 
Repaired.
Max Health can be increased by 
Max HP Boost and decreased by 
Unhealable Damage.