An ability can be used actively through the tapping on mana or is applied passively.
Active abilities cost Mana to use. Active abilities can apply Damage (typically between 0 and 12), have a range (typically between 1 and 2), and can target single or multiple targets. Multiple target damage is typically applied in terms of an area of effect (AoE). Some active abilities can also apply Status Effects.
In order to cast an ability, you have to cover the mana cost by tapping the required mana from your Mana Pool. Additionally, there is a Range the attack can reach relative to the caster. The target must be within range to inflict the stated damage. AoE attacks, denoted by the AOE symbol on the ability, attack all enemy units within range, as oppose to the default ability targeting only one unit within range.
The damage amount is removed from the target's Health. When the Health goes to 0, that target is Vanquished, and gets sent to the Beyond.
Passive ability are inherent to specific tamers or anima. They do not cost mana to use.
Some Structures can be upgraded, specifically Castles, but often Buildings as well. Upgrades require placing the mana cost of the upgrade onto the structure from your Mana Pool, and removing 1 Mana from the card back to your Mana Pool during your Upkeep phase. While a Structure is being upgraded, the other abilities on that card cannot be used. Once all Mana is returned to the Mana Pool, the Upgrade takes effect.
Upgrades can raise a Structure's Health, let it acquire new abilities, increase stats of other units in play, and more.
Abilities have a Range, which is the max number of Tiles the target must be located relative to the caster. The ability can be cast even if there are other units between the caster and the target.
Abilities with Area of Effect (AoE) apply damage to all enemies within Range. For example, an ability with a Range of 1 and AoE targets all enemies adjacent to the caster.
Similar to diagonals in Mobility, an ability must have a Range of at least 2 to target a diagonal Tile.