Hint: This goes in character discussion. Also, why does anything appeal? If you can answer that, you can answer why Derpy has appear for people, and trust me, the former is a much easier question to answer.
We all want to be DJs, of course! Derpy Hooves (formerly Ditzy Doo) was originally an Easter egg background character. Because of her eyes, and proneness to accidents or clumsiness, she is often depicted as anything from clumsy to mentally challenged. I honestly hate that and just like to think she's a goofy, comedic character no more than Pinkie Pie's natural personality.
What's not to get? Derpy's a forum admin. (I'm sorry, I'm a terrible person.) Anywho; Derpy, the appeal is in the derp. In a TV show whose target demographic Is the age of 5.
Okay...so we're talking WAAAAY back when God was a lad...Derpy was first seen in the background of the Episode 1 party at Twilight's library, with her eyes "derped" for the first time ever. This was noticed by several /4/chan users who dubbed the show to be "My Little Derpy" and from there she adopted the name "Derpy Hooves" over time. Her appeal is in that she is a sort of unintentionally included internet meme, I think what most people love about her is more about what the fans have come up with moreso than the show. Take for example this comic. (Yes Im sorry its sad) Spoiler: Lagging? Please... So, from just that one comic we see many appeals of Derpy; She has grown into a mane character of her own right, she has her own title as the most dependable mailmare in equestria. We also see that because of her eye condition other ponies tend not to have a lot of confidence in her, for all the right reasons of course however: in "Winter Wrap Up" she did go North to get the Southern birds [this is entirely at viewer discression, Im just using Derpy = Ditzy in this one case] and as such, with the story of all WWU's being like that, its a recurring theme that Derpy isnt the cleverest of ponies. So I think her appeal is in what each viewer makes of her, I think the comic above sums up my feelings about Derpy, (the lonely and sad, but brave and determined mare). You dont have to agree with it because it may not be entirely accurate to think about in a children's show. And Lastly, because of the Derp eyes, Derpy has a direct relation to internet fandom much in a similar way to Flutterrage and the Rage face. The reason Octavia/Vinyl Scratch/Colgate/Berry punch dont take off with Derpy is that they have had their stories written by the MLP producers instead of the fans, I never saw Octavia pull a trollface, or Vinyl do the Y U NO face, so they arent as relatable in the same way Derpy is.
I agree, I thought the original animation flaw was funny, but the whole cult following is a bit weird to me.
I didn't get Derpy either. Then I saw this: [video=youtube;SJ-btIKYeXA]http://www.youtube.com/watch?v=SJ-btIKYeXA[/video] Then I got it. She's a fan-creation built on a fluke; bronies thrive on empires built on flukes. The derpy fandom is the whole brony fandom in microcosm <3
I think a lot of the appeal seems to lie in the fact that Derpy/Ditzy/whatever represents the fact that the staff pay attention to the fandom; I read somewhere that the derped eyes in the first episode were just an animation joke, but the fandom loved the character so much that they put her in more scenes (complete with the eye derp).
Derpy showed us that it's okay to be who we are, no matter how we look, talk, or act. She showed us that we all make mistakes, and that they build us up. She showed us that, though people try to knock us down and take us out of this world, we all have our "fans" to catch us if we fall. This is why we love her, and why she'll live forever in our little brony hearts.