Where does the "quint" in "quintessential" come from?

Solution 1:

"Essence" in this context is a synonym for "element", and "essential" for "elemental". In pre-atomic theory, there were four "known" elements or essences — Earth, Air, Fire and Water — and a putative fifth element (quinta essentia). The fifth element was believed to be superior to the others, and so, "quintessential" has come to mean something that is superior.

Solution 2:

Somewhat missed in the answers thus far: the "fifth essence" is in fact identical to the "æther" of yore; said to be the stuff the stars and other heavenly bodies are made of. Thus, anything composed of the "fifth essence" had to be exceptional.