Race

God

Overweening Superiority · levels at 2 / 4 / 6 different pieces

2
All allies: skill cooldowns -40%.
4
All allies get another -40% skill cooldown. It multiplies with the (2) bonus, for -64% in total.
Note: The tooltip text is the same as level 2, and doesn't say the two levels multiply (-64% total, not -80%).
6
All allies: right after casting their skill, the remaining cooldown of that skill and of all their items is cut by 60%.

What the cooldown reduction affects

The (2) and (4) bonuses are given at the start of each battle to every friendly piece on the board. Together they cut cooldowns to 36% of normal (0.6 × 0.6). They work on a piece's own skill, but many other timers in the game are fixed and ignore them.

Reduced

Every piece's own skill, when it casts it normally.
Skills with special cooldown handling that the game scales for Gods: Jakiro's Ice Path and Macropyre, Invoker's Invoke, Mars's Bulwark and Gyrocopter's Flak Cannon.

Not reduced

Item cooldowns (Hand of Midas, Force Staff and other active items). The (6) bonus does shorten them after a skill cast, see below.
Tauren totems. They are summoned just after battle-start buffs are given out, and they trigger on a % chance with a tiny fixed internal cooldown anyway.
Draenei: the (2) drain runs on a fixed 4-second timer, and the (4) healing burst has a fixed 5-second cooldown.
Other synergy timers, such as the Elf (9) illusion and the Satyr fear cooldowns.
Summons and illusions created during the battle. They don't receive the God buff.

The (6) bonus is different

Half a second after a piece with mana casts its skill, the remaining cooldown of that skill and of all its items is cut by 60%. This is the only way Gods shorten item cooldowns.

Official in-game tooltip

SPECIES TRAIT: Overweening superiority
Active when you have at least (N) different pieces of this species on board. (Multiple effects stack)

(2)Gods: All allies get the effect: skill cooldown time -40%.
(4)Gods: All allies get the effect: skill cooldown time -40%.
(6) Gods: All allies get the effect: Using skills that consume mana will reduce the current remaining cooldown time of active abilities and items by 60%.

The highly worshipped Gods are considered as the creators of Drodo Island. Being both arrogant and prideful, the loyal beliefs from their creations have forged the supreme powers that Gods possess, granting them the most significant potential among all creatures which can completely change the outcome of a battle.