Her googley eyes that was made by mistake resembled an internet terms called 'Derp' which make so many internet-folks going hype on it. Since then, she appears in the episodes as a Waldo-like characters and even got her speaking role as a tip to the fans. The beauty of the character, as rumikoholic mentioned also lies in the fact that she had no background story, thus allowing the fans to use their imaginations to build her own story; a trait that is shared by many background pony.
Derpy's real name is Ditzy Doo. I think her appeal comes from the fact she had no real story. She was simply a mistake placed in the background of early FIM episodes. She's one of several background ponies who all gained popularity for similar reasons.