It's basically the "essence" of all the cards in a spread, numerologically derived.
You add up the numerical values of all the cards in the spread (some figure in the court cards, counting them as 11, 12, 13 1nd 14, others don't use them.) Some subtract the value of reversed cards, others don't. (Note that, if you don't subtract, you can never get down to zero - the Fool - so some just treat the Fool as Trump #22; also, using subtraction can give you a reversed quintessence card.) If you wind up with a number larger than 21 (or 22 as noted), subtract 9 from the total as many times as necessary to get down within that range. Then select the Trump card associated with that number as the quintessence (or "quint") card. (It's also possible to subtract all the way down to a single-digit number from 1 to 9.)
I've only been using them for a couple of months, so I'll let others with more experience with them describe how they read them. I just see them as kind of a "signature" or "keynote" for the spread that augments the outcome card and maybe gives a broader perspective on how it will manifest. I only use them if the outcome card is ambiguous, and only with smaller spreads.