Health (commonly known as HP, an abbreviation for Health/Hit Points) is the amount of life a unit or structure has. Max health is the cap on life any unit can have. Current health is directly reduced by damage and is regained in many different ways.
Every unit and structure has their max and current health displayed as a bar above their models. When displayed over a hero's model in game, the health meter is displayed as segmented bars.
Additionally, for your own hero, it is represented in the interface as a green bar with two numbers ( # / # ): the first one represents the actual life available at the moment, while the second is the maximum amount of health the hero can have. If a hero's health reaches zero and it doesn't have any abilities preventing it, death will occur. Max health scales additively with every bonus health point and increases with each level, meaning that each bonus point acquired directly affects the stat.