Cooldown on abilitiesAugment
A cooldown is how many turns you need to wait before the ability becomes usable again. Strong abilities such as Deflect and Lay Hands have a large cooldown so they may only be used once or twice while the champion is out.
Cooldown on Runes (in the runedock)Augment
The cooldown for a spell in the rune dock is how many of your turns you need to wait before casting it again. The cooldown for champions/spells/equipment is how many of your turn turns after it was destroyed, until it can be redeployed/reused.
To calculate this for a particular rune, take the cost divided by 5, rounded down. So Fight in Formation costs 30 nora, and thus has cooldown 6. Soulbleeder has cost 80, and so its cooldown is 16. Champions generally have higher cooldowns than other runes because their nora cost is higher.