c. 1300, "immediate influence of God or a god," especially that under which the holy books were written, from Old French inspiracion "inhaling, breathing in; inspiration" (13c.), from Late Latin inspirationem (nominative inspiratio), noun of action from past-participle stem of Latin inspirare "blow into, breathe upon," figuratively "inspire, excite, inflame," from in- "in" (from PIE root *en "in") + spirare "to breathe" (see spirit (n.)). ,
And the Lord God formed man of the dust of the ground, and breathed into his nostrils the breath of life; and man became a living soul. [Genesis ii.7]
The sense evolution seems to be from "breathe into" to "infuse animation or influence," thus "affect, rouse, guide or control," especially by divine influence. Inspire (v.) in Middle English also was used to mean "breath or put life or spirit into the human body; impart reason to a human soul." Literal sense "act of inhaling" attested in English from 1560s. Meaning "one who inspires others" is attested by 1867.
fount on Mount Helicon sacred to the Muses, its waters were held to bestow poetic inspiration, from Greek Hippokrene, earlier hippou krene, literally "horse's fountain," from genitive of hippos "horse" (from PIE root *ekwo- "horse") + krēnē "fountain," which is of uncertain origin.
1660s, member of the Protestant sect founded c. 1651 by English tailor Lodowicke Muggleton (1609-1698) and John Reeve. Members believed in the prophetic inspiration of the two founders as being the two witnesses mentioned in Revelation xi.3-6. Members were still living in the 1860s.