An Epic Riff is the piece of instrumental flair that lays the foundation of an entire song, and immediately recognizable from a small fragment, even by those who don't generally follow the type of music its from (even if they can't identify which song its from). For example, even people who are not fans of rock will probably recognize "In-A-Gadda-Da-Vida" by Iron Butterfly. 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?" Five people identified it, "it" being two chords on a steel guitar, as the start of the opening riff of Bob Dylan's "Lay, Lady, Lay" – from an audio clip literally less than two seconds long. That's an Epic Riff.
Please note that because ANY song could be this for someone, this page has no examples.