Etymology: About 1600, from Greek ataraxia (impassiveness).
The term is most often used in the discussion of Greek philosophy, with some variations of meaning: Epicurean ataraxia is a state of tranquility achieved through the pursuit of pleasure (according to Wikipedia, the Epicurean way to attain pleasure is to "live modestly and to gain knowledge of the workings of the world and the limits of one's desires"); Pyrrhonian ataraxia results from universal skepticism and a suspension of judgement.
I first noticed the word in a 2007 creative writing contest; it was one of ten words and phrases that were to be used (correctly) in a single poem, story, or essay. I was intrigued, crammed all ten into a respectable (IMO) two-stanza poem...then missed the deadline for submission. Well, it was good fun anyway.
from A Beginner's History of Philosophy, by Herbert Ernest Cushman:
There are three steps leading to Epicurean happiness: (1) the desire or the pain of unsatisfied craving; (2) the positive pleasure that removes the pain of unsatisfied desire; (3) ataraxia, the repose of the soul or true happiness.
"Repose of the soul"...that does sound nice.