Popular generally resonates with the 'general public'. Usually a piece has a very distinct part that is so catchy (in pop music today, we call it the 'hook' haha). Fur Elise has that opening bar that EVERYONE knows. Beethoven probably didn't write it with the same intent as pop artists do today; but we can't deny that a piece is catchy as all hell.
It's still the same piece it was however long ago it was written; so pieces like the Moonlight Sonata 1st movement, Fantasie Impromptu, la Campanella, Flight of the Bumblebee, Revolutionary Etude are just so well known because they just 'sound cool' to a lot of people. These are not popular pieces because every person on the planet can play them. It is just that they are undeniable catchy

If you meant more for rep choices being popular... it's probably something along those same lines. EVERYONE at my University wanted to play Jeux d'Eau. Most people had only become familiar with playing Ravel recently, and had naturally gravitated towards that piece. It's just got such a cool sound, so different than Mozart/Beethoven/Bach. People are a little thrown off by Scarbo at first listen, because they don't know what they are hearing, but the sparkly quality to Jeux d'Eau just makes it easier for the average person to listen to.
I'm rambling.