If something “fills” or “fits the bill,” it’s satisfying, whether it’s a good meal or a job well done.
The expressions come from the days when theatrical advertising was done through handbills or posters.
“Filling the bill” meant adding acts to pad a weak program.
But if a single star could pull in an audience through his or her individual fame and talent, their name was all that was needed so it was enlarged to fit the bill.