Health (also hit points (HP)) refers to the amount of damage on creature can endure before it dies. For example, a pikeman has maximum health of 10. which means that a stack of 10 pikemen will have 100 points of health. If another stack deals 25 points of damage to the pikemen stack, it will lose two of its pikemen. The damage is always dealt to all the "topmost" creatures, which means that after the attack, the pikemen stack will have seven pikemen with health of 10 and one pikeman ("the topmost") with health of 5.
Health also determines the amount of experience a winning hero will receive after each combat.