Evolution Essence is an item that was introduced with Enlightenment which makes it easier for you to fulfill the prerequisite that you must get your Hero to Pisces Evolution before they can be Enlightened. Every Hero who has Enlightenment unlocked has their own Evolution Essences which are currently only obtained through Events. Evolution Essences are used to bypass all of the resource and level requirements of Evolution. So all you need to unlock a level of Evolution are the required amount of that Heroes Essences.
Obtaining Evolution Essences
During Lords Gone Wild and The Wishing Tree Events you receive points equal to the amount of Jewels you spend during the Event. The points can be used to buy a variety of items, very commonly among those items are stacks of 20 Evolution Essences for 4k or 5k points and occasionally 10 essences for 1k points. The trick is that Jewels spent on trades in Limited Time Trading are considered as spent, even the trade Jewels for Jewels. So you can trade 15k or 16k Jewels for 20k Jewels, and receive 15 or 16k points in whatever spend Events are running at the time.
Using Evolution Essences
Once you have some of the Heroes Evolution Essences a check box will appear on their Evolution page. checking the box tells the game to use the essences rather than the normal resources.