1580s, "pertaining to or constituting a lengthy heroic poem," via French épique or directly from Latin epicus, from Greek epikos, from epos "a word; a tale, story; promise, prophecy, proverb; poetry in heroic verse" (from PIE root *wekw- "to speak").
Extended sense of "grand, heroic" is recorded in English by 1731. From 1706 as a noun in reference to an epic poem, "A long narrative told on a grand scale of time and place, featuring a larger-than-life protagonist and heroic actions" [Miller Williams, "Patterns of Poetry"]. Earlier as "an epic poet" (1630s).
I believe the word 'epic' is usually understood by English readers to mean merely a long and grand poem instead of a short slight one—at least, I know that as a boy I remained long under that impression myself. It really means a poem in which story-telling, and philosophical reflection as its accompaniment, take the place of dramatic action, and impulsive song. [Ruskin, "Elements of English Prosody, for use in St. George's Schools," 1880]