Well, to break it down shortly in a way that will definetly get my ass staked for the choice of words:
She is a mysterious musician with almost no background story other than a small buildup to explain why she is demacian, she is this all friendly, shy mute personality, basically the "Cute" anime girl, she is confirmed to have league's biggest bust size and is basically THE model image when any halfway sane hormonal teen tries to imagine league characters without clothes, and she has had consistent popularity spikes in picks regarding lanes and Item builds. Jungle is literally the only place she's not been meta in at least once and she only barely avoided being so. And her hair resembles Hatsune Miku.
Then there is everything about her more scoped appearances and characteristics. She has, as you can hear from her vo's, a voice made by angels for fucks sake, literally she is the morgan freeman of league of legends. She also is very mature and pure, which adds an instinctual, more subconcious and carnal attraction. The way she is drawn and described, her eyes, her chinline, her facial proportions even her eyebrows are the very textbook definition of an Aphrodite, she is designed to be so pretty that even guys get jealous at her. and the worst thing is, i don't even like her, riot is just REALLY GOOD at making her character profile overloaded, but still fully functional. She is in almost every sense the stereotypical "Ideal" woman.
And we know how human psyche works, they aspire for things they cannot have. because there is no such thing as an ideal woman, sona becomes this massive clusterfucks of things we really want, which transcends into a deep state of passion which then translates into admiration and BOOM you are now a fan of her even if you hate her.
A good example for that is swain btw, he hates her as a person, but he cannot even try to deny her skill and grace and talent in both music and magic.
And as some people said, she is a stereotype egirl pick. Most popular streamers that play her are female, including the biggest female shot in lol's twitch bank, pokimane.