To me it's any flight that starts at night (i.e. when it is dark) and ends the next day (when the sun is up or is about to come up). I would call AS 172 JNU-SEA 0110-0425 a redeye.

Or maybe it's just any flight where you end up at the Redeye Grill at 56th and 7th in Manhattan. Mmmmm....dancing shrimp!