If you drop a guitar down a flight of stairs, it'll play 'Gloria' on its way to the bottom.
An Epic Riff is that piece of instrumental flair that lays the foundation of an entire song, and is immediately recognizable from a small fragment, even by people who don't generally follow the type of music it is from (even if they can't identify which song it's from). For example, even people who are not fans of rock will probably recognize "In A Gadda Da Vida" by Iron Butterfly (even if they think it's by Black Sabbath). They may not know the name of the band; they may not even know the name of the song; but they'll say "Oh, yeah, it's that song!" when they hear it, and they'll be thinking of the right song.
To provide an example: a person once posted a request for help on a blog. The gist of the post was "I can't figure out what song this is. The tape label says it's called "Portrait of a Gentle Young Girl". Help?" 5 people identified it, "it" being two chords on a steel guitar, as the beginning of the opening riff of Bob Dylan's Lay, Lady, Lay—from an audio clip that was literally less than 2-seconds long. That's an Epic Riff.
See Fanfare for the orchestral equivalent.
Please note that because any song could be this for someone, this page has no examples.