From Dictionary.com:
ep·ic Pronunciation Key (pk)
n.
An extended narrative poem in elevated or dignified language, celebrating the feats of a legendary or traditional hero.
A literary or dramatic composition that resembles an extended narrative poem celebrating heroic feats.
A series of events considered appropriate to an epic: the epic of the Old West.
adj.
Of, constituting, having to do with, or suggestive of a literary epic: an epic poem.
Surpassing the usual or ordinary, particularly in scope or size: “A vast musical panorama... it requires an epic musical understanding to do it justice” (Tim Page).
Heroic and impressive in quality: “Here in the courtroom... there was more of that epic atmosphere, the extra amperage of a special moment” (Scott Turow).
\Ep"ic\, a. [L. epicus, Gr. ?, from ? a word, speech, tale, song; akin to L. vox voice: cf. F. ['e]pique. See Voice.] Narrated in a grand style; pertaining to or designating a kind of narrative poem, usually called an heroic poem, in which real or fictitious events, usually the achievements of some hero, are narrated in an elevated style.
The epic poem treats of one great, complex action, in a grand style and with fullness of detail. --T. Arnold.
Source: Webster's Revised Unabridged Dictionary, © 1996, 1998 MICRA, Inc.
epic
adj 1: surpassing the ordinary especially in size or scale; "an epic voyage"; "of heroic proportions"; "heroic sculpture" [syn: heroic, larger-than-life] 2: constituting or having to do with or suggestive of a literary epic; "epic tradition" [syn: epical] n : a long narrative poem telling of a hero's deeds [syn: epic poem, epos]
Source: WordNet ® 1.6, © 1997 Princeton University
HYPOTHESIS: An epic campaign is like the stories involving Beowulf, Cuchulainn, Hercules etc.
OBSERVATION: These legends strike me to an extent as being just hero worship of the form "He was so strong and tough and indomitable that he could do X. What a hero."
ASSUMPTION: The tales of Beowulf, Cuchulainn and Hercules are effectively an early example of the guy who accosts you at the convention and tells you all about how elite his 30th level fighter is and what he did and won't shut up about it.
CONCLUSION: If you think your epic level campaign is all about how powerful and invincible your characters are and the neato things they can do, you're historically correct in the terms of portraying "epic".