late 14c., an astrological term, "streaming ethereal power from the stars when in certain positions, acting upon character or destiny of men," from Old French influence "emanation from the stars that acts upon one's character and destiny" (13c.), also "a flow of water, a flowing in," from Medieval Latin influentia "a flowing in" (also used in the astrological sense), from Latin influentem (nominative influens), present participle of influere "to flow into, stream in, pour in," from in- "into, in, on, upon" (from PIE root *en "in") + fluere "to flow" (see fluent).
The range of senses in Middle English was non-personal, in reference to any outflowing of energy that produces effect, of fluid or vaporous substance as well as immaterial or unobservable forces. Meaning "exertion of unseen influence by persons" is from 1580s (a sense already in Medieval Latin, for instance Aquinas); meaning "capacity for producing effects by insensible or invisible means" is from 1650s. Under the influence (of alcohol, etc.) "drunk" first attested 1866.
1630s, atmosphaera (modern form from 1670s), "gaseous envelop surrounding the earth," from Modern Latin atmosphaera, from Greek atmos "vapor, steam" (see atmo-) + sphaira "sphere" (see sphere). In old science, "vaporous air," which was considered a part of the earth and a contamination of the lower part of the air (n.1).
Þe ouer partye of þe eyr is pure and clene, clere, esy & softe, ffor mevynge of stormys, of wynde and of wedir may nat reche þerto; and so it perteyneþ to heuenlych kynde. And þe neþir partye is nyʒe to þe spere of watir and of erþe, and is troubly, greet and þicke, corpulent and ful of moyst erþy vapoures, as longiþ to erþy partyes. Þe eyr strecchiþ hym kyndely al aboute fro þe ouer partye of þe erþe and of watir anon to þe spere of fire. [Bartholomew Glanville, "De proprietatibus rerum," c. 1240, translated by John of Trevisa c. 1398 ]
First used in English in connection with the Moon, which, as it turns out, practically has none.
'Tis Observed, in the Solary Eclipses, that there is some times a great Trepidation about the Body of the Moon, from which we may likewise argue an Atmo-sphaera, since we cannot well conceive what so probable a cause there should be of such an appearance as this, Quod radii Solares a vaporibus Lunam ambientibus fuerint intercisi, that the Sun-beams were broken and refracted by the Vapours that encompassed the Moon. [Rev. John Wilkins, "Discovery of New World or Discourse tending to prove that it probable there may be another World in the Moon," 1638]
Figurative sense of "surrounding influence, mental or moral environment" is c. 1800.