There is a tooltip, but it's only on the production screens for singles/shows. Cute gives a bonus to hardcore/male appeal for the single/show, cool gives one to hardcore/female, sexy gives one to hardcore/male, pretty gives one to hardcore/female, dance gives one to casual/male, vocals gives one to casual/female, funny gives one to casual/male, smart gives one to casual/female and team chemistry gives a small bonus to everyone.
The influence stat is levelled up by doing auditions, talking to idols, and I think taking loans. I think it effects how good idols you get at auditions are, or at least they seemed to be way better when I'd got up to rank 5 for my second round of idol auditions (using the same audition level).