There are two explanations as to what a One-Eyed, One-Horned, Flying, Purple People Eater is. The first is a term reffering to a sexually active male. Hence, "one eyed, one horned" is reffering to the male reproductive organ. It is also noted that when listening to the song about One-Eyed, One-Horned, Flying, Purple People Eaters while beleiving it to be a term reffering to a sexually active male, you may find the song even more amusing then you at first found it. As to the "flying, purple people eater" part, this reffers to when said male is extremely shitfaced and decided to please his female.