I know there have been about twenty bajillion different attempts to describe essence, most of them from people who have done essence for about a bajillion years themselves. (Like Jay.

) Though they know it very well, it can be hard for a newbie to understand all the terms and stuff...so I thought maybe I'd try (from a newbie's point of view who's only done two maps) to explain essence for the other new people.
(And moderators, if you think this is a dumb idea, feel free to remove the thread)
So what is essence? It's kind of like a nested list of feelings that you get upon thinking about your character. Essence is like the impressions you get about something upon hearing it's name or reading about it. And everyone's impression of each object's essence will be different. But mainly, essence is designed for helping you to communicate to other writers (who understand what essence is).
So, sounds good, but where this party gets complicated is actually writing the stuff.
SUBJECT
ASPECT
___{Qualifier
______[Characteristic
_________(metaphor)
______]
___}
So let's take this apart piece by piece and see what each thing means. Subject is really very easy, it's sort of the title of the essence map. For example, the subject could be the name of your character, or a specific city in a novel or something.
An aspect kind of narrows it down some more. Rather than just listing tons of metaphors that come to mind when one thinks about the character, an 'Aspect' narrows it down to some smaller categories (such as 'body', 'mind', 'soul', and 'spirit').
A qualifier kind of narrows down an aspect even more. For example, if your aspect was 'Mind', then your qualifier could be 'Strength'. So it narrows it down from you listing all the metaphor's about the characters mind to listing the metaphors about the strength of the character's mind.
Again, a characteristic narrows it down even further. For example, 'trust' could be a characteristic, and would then be a list of metaphors about the strength of the trust in the character's mind. Characteristics are usually the only section in which you directly list metaphors.
I like the way Jay (Sir Emeth) put it. Think of the subject as a big box. You can put smaller boxes inside the box, (these are the aspects) But then you've still got a ton of junk in each of these smaller boxes, so you put some smaller boxes in these (these are the qualifiers). And if those boxes still have tons of stuff, you put smaller boxes inside those (these are the characteristics). Finally, these smallest boxes are what you put all of your stuff in, and it's all sorted nicely.
Anyway's, here's an example part of an essence map. The important part to remember is that you can have as many aspects, qualifiers, characteristics and metaphors as you want! You're only limited to as many as your imagination comes up with:
GRIZZLY BEAR
BODY
___{Strength
______[Legs
_________(strong as an oak)
_________(powerful as a dinosaur's neck)
______]
______[Teeth
_________(hard as diamond)
_________(sharp as needles)
______]
___}
___{Cunning
______[Eyes
_________(quick as a fox)
_________(a glittering sunset)
______]
______[Ears
_________(sensitive as a hare's ears)
______]
___}
Notice how there are several qualifiers inside the aspect (Strength, Cunning), and several characteristics inside each qualifier (eyes, ears, teeth, legs). But it's only inside of characteristics that we list metaphors, such as (sensitive as a hare's ears)
So that's all essence is, it's kind of a cross between an outline and a list of metaphors, and it's just a standardized way for you to take apart your character that other writers can understand. If you have any specific questions, I'm probably not the person to ask, but I'll try my best to answer questions. And experienced essence people, if I'm totally off the mark with this topic, let me know as well. This is just the way in which I understand essence, and it might be wrong.
