Hazard insurance covers damage to the physical structure of the home or the "hazards" a home could face. This is what hazard insurance covers:

Fire damage. If a home is damaged in a fire, hazard insurance will cover the cost of repairing the structure itself.
Hail. Large hail or heavy hail storms can cause damage to many things, including a home. Hazard insurance covers that damage.
Lightning. Lightning strikes are rare, but they can cause significant damage. Hazard insurance covers the damage from the strike and potential fires.
Theft. If a home is damaged from a theft, hazard insurance covers it. Other parts of a homeowners insurance policy will cover the stolen property.
Vandalism. If a home is vandalized, hazard insurance will cover the damage.
Fallen trees. Storms can cause trees to fall over, and hazard insurance can protect against the damage that would cause.
Explosions. Gas leak explosions can cause extensive damage to a home. Luckily most explosions are covered by hazard insurance.
Vehicle damage to a home. Rarely, a vehicle will collide with a home. Hazard insurance often covers the damages to the home should that happen.

Homeowners insurance policies—and therefore the hazard insurance portion—are all different, so different hazards may be covered under a certain policy.