I'm a casual player of League of Legends, but I have yet to pay for anything that the game offers. Between the free to play champions and those I purchase with my influence points, I have enough to play normal matches, which is all I do. While I probably could use a larger pool of runes to make my early game a bit easier, I prefer spending my IP on champions and don't imagine that RP would be any different. I've never seen a point into sinking money on skins, until I saw my brother play a game with a DJ Sona. Upon seeing it, I seriously considered getting the RP to buy it. I'd never cared about skins before, so why was this different?
With normal skins, your characters appearance, animations and wards can change but aside from possibly looking marginally cooler (and confusing your opponent with skins that look like other characters...) nothing has really changed. You're playing the same game, with mechanically identical characters in different costumes. Or sometimes even just different colours in some cases, like Special Weapon Zach. So the answer to my question feels rather obvious; The DJ Sona skin adds to the game experience.
For those who don't know; having a DJ Sona in the game changes the background music. Personally, I don't like the default background music. It kinda feels like a less dramatic version of the Game of Thrones intro, so I'll often mute the in-game music and have my own playing instead. The DJ Sona music is a great improvement and matches the tone of the game a lot better.
I was much more willing to buy this skin than any other because it adds something to the game. The new music and associated tone greatly alters the game experience, which therefore makes the game more enjoyable. This leads me to the conclusion that if Riot were to offer ways of changing or improving the gaming experience with future skins, they would sell a lot better.