I can't say what makes everyone like her but for me (and some things are repeated of course):
-- her lyrics are awesome... be it happy and upbeat or sad and slow, each song to me is so unique and so personal and I love that.
-- her diversity... for one, I love that she sings all kinds of songs, happy, sad, trance, dance, rock-sounding songs, bubbly.. that's great, I never get bored of her ever changing style.
-- her ever-changing style haha... I love the fact that she's changes and grows
-- her fashion sense... well of course I like her because she knows how to dress, and dress well and also that she changes her look every now and then... like regular people do.
-- her sincerity... I love the fact that she seems so sincere and down to earth. Even though she's a Pop Star, she's not the "holier than thou" type, and really knows how to connect with the people listening to her music.
-- her hardworking-ness... I admire the fact that she writes most of her lyrics, controls a lot of her musical direction and just all around works hard despite a lot of hardships. she really gives it her all, and we can see.
-- I also admire the fact that she's been able to get through a tough beginning and is really a great example of how a bad beginning doesn't mean a bad future.
-- Lastly (and I'm sure there are more but I just can't think of em xD) I love the fact that she is marketable. I like knowing that she has posters and all sorts of collectibles, that she's in CMs and all sorts of other stuff because, well, I just love that.