"Furthermore, by using Essences obtained from demons, you can transform you and your allies' skills and affinities."
Essences generally represent the titular demon's regular properties in the shape of special consumable items (for instance, "Agathion's Essence.") This includes all of their skills and affinities. Essences are the base subject of Essence Fusion, a process accessed within the Apothesis tab.
Essences can be used to modify the skill set of either the protagonist or any ally demons, and even let the protagonist himself the ability to modify his affinity chart. Although skills can be handpicked, letting the party member inherit any skills as pleased, the chart can only be copied in its entirely, which includes weaknesses.
The ability to implement skills is greatly restricted at first, and will need the "Art of Essences" Miracles to unlock the skill pool. Without the miracles, only the demons' innate skills as of their recruitment can be unlocked, with each Art of Essences unlocking the skills they can unlock by leveling up once. The maximum is 3 levels, in which case all skills will be unlocked.
Demons are able to give their own Essences in battle after leveling up and quests, and they can also be found in Treasure Chests and Search Points. Cornered demons in the wild will offer their Essence once a certain Miracle is purchased.
There are also certain Essences of entities that cannot be recruited as party members. There are multiple variants of Aogami, all of which grant their own sets of skills, in addition to the unique skills exclusive to the Nahobino race, or for the party, can only be taught by the protagonist. All unique skills are innate, and as such do not require any additional Miracles to be learned.
Additionally, in the "Return of the True Demon" DLC, the Demi-fiend also has an Essence of his own, that will be dropped upon defeating him.