Some Guardians can grant your troops a special type of damage: fire, ice or earth.
Elemental Damage System
This type of damage is defended with their corresponding resistance element.
Fire is strong against ice, but weak against earth.
Ice is strong against earth but weak against fire.
Earth is strong against fire, but weak against ice.
Like other stats, elemental damage can be a fixed increase or a multiplier depending on the related Guardian skill. You will see the total elemental damage displayed as the Guardian Bonus when setting up a march.
When to use it
Attacking a city can be very hard if the defending army has tons of defending units. A smart way of weakening the army enough to break their defense is by sending some attacks with high elemental damage and defense.
Sending troops to farm resources can be dangerous sometimes, especially in the inner part of the map. By sending an elemental Guardian and some defending troops with them your troops will be more protected when collecting resources.