Hit points refer to a unit's health. When a unit is first constructed it has full hit points. When a weapon hits that unit, the weapon does damage that reduces the unit's hit points. When a unit's hit points reach 0, the unit is destroyed. Units with more hit points are harder because they can withstand more damage before they are destroyed.
Shields also have hit points, and they are also reduced by damage. When a shield's hit points reach 0, the shield collapses and any units inside the shield are vulnerable. This shield must recharge for a short period, and then its hit points are restored to its maximum.