Essence is the most pure component of an object - it's "all that's left when you extract everything but the idea of the thing."
There are 24 different Essences, and they are used for creating new Buildings in the Town management menu, and for crafting new World Seeds by talking to Coppertop and using the alchemy tab.
Essences can be aquired by growing plants and harvesting other things in the various Worlds grown from world seeds, or by completing Goals or by deconstructing items using Coppertop. You can also purchase certain, and limited, essences from the Everkin using EverKoin.