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.

type of infectious disease, now known to be caused by a virus, usually occurring as an epidemic, with symptoms similar to a severe cold along with high fever and rapid prostration, 1743, borrowed (during an outbreak of the disease in Europe), from Italian influenza "influenza, epidemic," originally "visitation, influence (of the stars)," from Medieval Latin influentia in the astrological sense (see influence).

AN Article from Rome informs us that a Sort of Plague has broke out there, which destroys Abundance of their People, and they call it the Influenza. [The Gentleman's Magazine, April 1743]

Used in Italian for diseases at least since 1504 (as in influenza di febbre scarlattina "scarlet fever") on notion of astral, occult, or atmospheric influence. The 1743 outbreak began in Italy. Often applied since mid-19c. to severe colds.

1610s, erroneous form of plenitude, probably by influence of plenty, etc.