Likable judges (the show's judges are larger than life characters who make the show a soap opera-- it's very important that the judges be mockable, which is why Paula Abdul can show up to work as drunk as she wants to be) and contestants (they have to be people you want to succeed-- or at least love to hate), features music people are generally acquainted with and mostly like, the first few weeks are schadenfreude and that's popular in the US, the following weeks feature people who are talented singers for the most part (we DVR the shows and watch them delayed and zip through the occassional really bad ones-- but AI knows that really bad singing in the voting rounds is not good for business, because people don't want to listen to 90+ seconds of really bad singing voluntarily so they try to get good singers through) and people like to hear talented singers, and finally the show needs the audience to help and the audience feels qualified to help (which is why this show is more popular than dance shows or whatever that are basically the same format-- this is very critical to the show's popularity).
AI tries to keep the show moving, which is important, too, for our ADD culture. They tweak things some every year, too, to keep it fresh.