c. 1500, "now existing;" 1580s, "of or pertaining to present or recent times;" from French moderne (15c.) and directly from Late Latin modernus "modern" (Priscian, Cassiodorus), from Latin modo "just now, in a (certain) manner," from modo (adv.) "to the measure," ablative of modus "manner, measure" (from PIE root *med- "take appropriate measures"). Extended form modern-day attested from 1872.
In history, in the broadest sense, opposed to ancient and medieval, but often in more limited use. In Shakespeare, often with a sense of "every-day, ordinary, commonplace." Meaning "not antiquated or obsolete, in harmony with present ways" is by 1808.
Of languages, indicating the current form of Greek, etc., 1690s; modern languages as a department of study (1821) comprised those now living (i.e. not Latin or Greek) that were held to have literary or historical importance. The use of modern English is at least from c. 1600 (in Cowell's "Interpreter," explaining an Anglo-Saxon word). The scientific linguistic division of historical languages into old, middle, and modern is from 19c.
Slang abbreviation mod is attested from 1960. Modern art is from 1807 (in contrast to ancient; in contrast to traditional, representing departure or repudiation of accepted styles, by 1895); modern dance is attested by 1912; modern jazz by 1954. Modern conveniences is recorded by 1926.
1580s, "person of the present time" (contrasted to ancient), from modern (adj.). From 1897 as "one who is up to date."