The BJ Challenge is where you compete with your girls against other players, make cash, and win rewards.
Each power level of a girl is determined based on 3 stats: Sex Appeal (power), Commitment (speed), and Tricks (chance).
You can increase these stats by buying equipment and by training your girls, using Practice, to increase their stats. You should focus on training just one girl, so you can use the Coaching option from the Practice menu to increase all stats of your other girls based on the stats of your main girl, at the same time.