Per the DragonVale wiki:
Activate: Kairos can be activated once every four days using the "Activate" button. Upon activation, activities in the park that require time to complete will be accelerated by six hours.
Ability to give gems to friends and the Colosseum are not accelerated.
Some tips to make best use of this ability:
- Be sure to have a full hatchery and both the Breeding Cave and EBI active. For maximum benefit, you'd want all of these to have more than 6 hours left (each egg, each breeding pair).
- Fill your farms with Pumpermelons or Dragon Fruit, or a similar long grow time treat. Especially if you don't yet have the Huge Treat Farm this will be a nice bonus.
- Harvest coins from all habitats. Especially for the lower capacity habitats, this may save you from hitting the cap once you activate the ability.
- Check the timer on the Kairos pedestal before spending gems to accelerate something. With such a long cool down, you may easily forget about him - and he's free!