A "regular" simile is a direct comparison between two essentially different things which share at least one common element, and it almost always uses the words like or as. An epic simile is the same, only it is a more extended (lengthy) comparison, suitable to the epic literature in which it is contained.
Book I of The Odyssey by Homer begins with a meeting of the gods, one of whom is Athena (or Minerva, in some translations). After she pleads her case that Odysseus should be allowed--finally--to go home, she leaves Olympus in a spectacular fashion:
[S]he bound on her glittering golden sandals, imperishable, with which she can fly like the wind over land or sea; she grasped the redoubtable bronze-shod spear, so stout and sturdy and strong, wherewith she quells the ranks of heroes who have displeased her, and down she darted from the topmost summits of Olympus, whereon forthwith she was in Ithaca....
Here is the epic simile. Athena straps on her famous and remarkable sandals and is immediately able to "fly like the wind" to her destination, in this case Odysseus's home in Ithaca. This is a terrific example of an epic simile.
The simile is repeated, in a way, when Athena leaves Telemachos, again in her spectacular fashion. Homer says she "flew away like a bird into the air," which is a clear continuation of, or at least a reference to, the simile which compares Athena to both the wind and something that can fly on the wind.
For more insights and analysis of The Odyssey, I have linked several excellent eNotes sites below for you.